Thomas Aquinas: Commentary on Aristotle's Metaphysics, Book 5: English

METAPHYSICS
BOOK V

DEFINITIONS

CONTENTS

LESSON 1: Five Senses of the Term "Principle." The Common Definition of Principle
LESSON 2 The Four Classes of Causes. Several Causes of the Same Effect. Causes May Be Causes of Each Other. Contraries Have the Same Cause
LESSON 3 All Causes Reduced to Four Classes
LESSON 4 The Proper Meaning of Element; Elements in Words, Natural Bodies, and Demonstrations. Transferred Usages of "Element" and Their Common Basis
LESSON 5 Five Senses of the Term Nature
LESSON 6 Four Senses of the Term Necessary. Its First and Proper Sense. Immobile Things, though Necessary, Are Exempted from Force
LESSON 7 The Kinds of Accidental Unity and of Essential Unity
LESSON 8 The Primary Sense of One. One in the Sense of Complete. One as the Principle of Number. The Ways in Which Things Are One. The Ways in Which Things Are Many
LESSON 9 Division of Being into Accidental and Essential. The Types of Accidental and of Essential Being
LESSON 10 Meanings of Substance
LESSON 11 The Ways in Which Things Are the Same Essentially and Accidentally
LESSON 12 Various Senses of Diverse, Different, Like, Contrary, and Diverse in Species
LESSON 13 The Ways in Which Things Are Prior and Subsequent
LESSON 14 Various Senses of the Terms Potency, Capable, Incapable, Possible and Impossible
LESSON 15 The Meaning of Quantity. Its Kinds. The Essentially and Accidentally Quantitative
LESSON 16 The Senses of Quality
LESSON 17 The Senses of Relative
LESSON 18 The Senses of Perfect
LESSON 19 The Senses of Limit, of "According to Which," of "In Itself," and of Disposition
LESSON 20 The Meanings of Disposition, of Having, of Affection, of Privation, and of "To Have"
LESSON 21 The Meanings of "To Come from Something," Part, Whole, and Mutilated
LESSON 22 The Meanings of Genus, of Falsity, and of Accident

LESSON I
Five Senses of the Term "Principle." The Common Definition of Principle
ARISTOTLE'S TEXT Chapter 1: 1012b 34-1013a 23
403. In one sense the term principle [beginning or starting point] means that from which someone first moves something; for example, in the case of a line or a journey, if the motion is from here, this is the principle, but if the motion is in the opposite direction, this is something different. In another sense principle means that from which a thing best comes into being, as the starting point of instruction; for sometimes it is not from what is first or from the starting point of the thing that one must begin, but from that from which one learns most readily. Again, principle means that first inherent thing from which something is brought into being, as the keel of a ship and the foundation of a house, and as some suppose the heart to be the principle in animals, and others the brain, and others anything else of the sort. In another sense it means that non-inherent first thing from which something comes into being; and that from which motion and change naturally first begins, as a child comes from its father and mother, and a fight from abusive language. In another sense principle means that according to whose will movable things are moved and changeable things are changed; in states, for example, princely, magistral, imperial, or tyrannical power are all principles. And so also are the arts, especially the architectonic arts, called principles. And that from which a thing can first be known is also called a principle of that thing, as the postulates of demonstrations. And causes are also spoken of in the same number of senses, for all causes are principles.
404. Therefore, it is common to all principles to be the first thing from which a thing either is, comes to be, or is known. And of these some are intrinsic and others extrinsic. And for this reason nature is a principle, and so also is an element, and mind, purpose, substance, and the final cause; for good and evil are the principles both of the knowledge and motion of many things.
COMMENTARY
Principle
751. Now it should be noted that, although a principle and a cause are the same in subject, they nevertheless differ in meaning; for the term principle implies an order or sequence, whereas the term cause implies some influence on the being of the thing caused. Now an order of priority and posteriority is found in different things; but according to what is first known by us order is found in local motion, because that kind of motion is more evident to the senses. Further, order is found in three classes of things, one of which is naturally associated with the other, i.e., continuous quantity, motion and time. For insofar as there is priority and posteriority in continuous quantity, there is priority and posteriority in motion; and insofar as there is priority and posteriority in motion, there is priority and posteriority in time, as is stated in Book IV of the Physics. Therefore, because a principle is said to be what is first in any order, and the order which is considered according to priority and posteriority in continuous quantity is first known by us (and things are named by us insofar as they are known to us), for this reason the term principle, properly considered, designates what is first in a continuous quantity over which motion passes. Hence he says that a principle is said to be “that from which someone first moves something,” i.e., any part of a continuous quantity from which local motion begins. Or, according to another reading, “Some part of a thing from which motion will first begin”; i.e., some part of a thing from which it first begins to be moved; for example in the case of a line and in that of any kind of journey the principle is the point from which motion begins. But the opposite or contrary point is “something different or other,” i.e., the end or terminus. It should also be noted that a principle of motion and a principle of time belong to this class for the reason just given.
752. But because motion does not always begin from the starting point of a continuous quantity but from that part from which the motion of each thing begins most readily, he therefore gives a second meaning of principle, saying that we speak of a principle of motion in another way “as that from which a thing best comes into being,” i.e., the point from which each thing begins to be moved most easily. He makes this clear by an example; for in the disciplines one does not always begin to learn from something that is a beginning in an absolute sense and by nature, but from that from which one “is able to learn” most readily, i.e., from those things which are better known to us, even though they are sometimes more remote by their nature.
753. Now this sense of principle differs from the first. For in the first sense a principle of motion gets its name from the starting point of a continuous quantity, whereas here the principle of continuous quantity gets its name from the starting point of motion. Hence in the case of those motions which are over circular continuous quantities and have no starting point, the principle is also considered to be the point from which the movable body is best or most fittingly moved according to its nature. For example, in the case of the first thing moved [the first sphere] the starting point is in the east. The same thing is true in the case of our own movements; for a man does not always start to move from the beginning of a road but sometimes from the middle or from any terminus at all from which it is convenient for him to start moving.
754. Now from the order considered in local motion we come to know the order in other motions. And for this reason we have the senses of principle based upon the principle of generation or coming to be of things. But this is taken in two ways; for it is either “inherent,” i.e., intrinsic, or “non-inherent,” i.e., extrinsic.
755. In the first way, then, a principle means that part of a thing which is first generated and from which the generation of the thing begins; for example, in the case of a ship the first thing to come into being is the base or keel, which is in a certain sense the foundation on which the whole superstructure of the ship is raised. And, similarly, in the case of a house the first thing that comes into being is the foundation. And in the case of an animal the first thing that comes into being, according to some, is the heart, and according to others, the brain or some such member of the body. For an animal is distinguished from a non-animal by reason of sensation and motion. Now the principle of motion appears to be in the heart, and sensory operations are most evident in the brain. Hence those who considered an animal from the viewpoint of motion held that the heart is the principle in the generation of an animal. But those who considered an animal only from the viewpoint of the senses held that the brain is this principle; yet the first principle of sensation is also in the heart even though the operations of the senses are completed in the brain. And those who considered an animal from the viewpoint of operation, or according to some of its activities, held that the organ which is naturally disposed for that operation, as the liver or some other such part is the first part which is generated in an animal. But according to the view of the Philosopher the first part is the heart because all of the soul’s powers are diffused throughout the body by means of the heart.
756. In the second way, a principle means that from which a thing’s process of generation begins but which is outside the thing. This is made clear in the case of three classes of things. The first is that of natural beings, in which the principle of generation is said to be the first thing from which motion naturally begins in those things which come about through motion (as those which come about through alteration or through some similar kind of motion; for example, a man is said to become large or white); or that from which a complete change begins (as in the case of those things which are not a result of motion but come into being through mutation alone). This is evident in the case of substantial generation; for example, a child comes from its father and mother, who are its principles, and a fight from abusive language, which stirs the souls of men to quarrel.
757. The second class in which this is made clear is that of human acts, whether ethical or political, in which that by whose will or intention others are moved or changed is called a principle. Thus those who hold civil, imperial, or even tyrannical power in states are said to have the principal places; for it is by their will that all things come to pass or are put into motion in states. Those men are said to have civil power who are put in command of particular offices in states, as judges and persons of this kind. Those are said to have imperial power who govern everyone without exception, as kings. And those hold tyrannical power who through violence and disregard for law keep royal power within their grip for their own benefit.
758. He gives as the third class things made by art; for the arts too in a similar way are called principles of artificial things, because the motion necessary for producing an artifact begins from an art. And of these arts the architectonic, which “derive their name” from the word principle, i.e., those called principal arts, are said to be principles in the highest degree. For by architectonic arts we mean those which govern subordinate arts, as the art of the navigator governs the art of ship-building, and the military art governs the art of horsemanship.
759. Again, in likeness to the order considered in external motions a certain order may also be observed in our apprehensions of things, and especially insofar as our act of understanding, by proceeding from principles to conclusions, bears a certain resemblance to motion. Therefore in another way that is said to be a principle from which a thing first becomes known; for example, we say that “postulates,” i.e., axioms and assumptions, are principles of demonstrations.
760. Causes are also said to be principles in these ways, “for all causes are principles.” For the motion that terminates in a thing’s being begins from some cause, although it is not designated a cause and a principle from the same point of view, as was pointed out above (750).
761. Therefore, it is (404).
Then he reduces all of the abovementioned senses of principle to one that is common. He says that all of the foregoing senses have something in common inasmuch as that is said to be a principle which comes first (1) either with reference to a thing’s being (as the first part of a thing is said to be a principle) or (2) with reference to its coming to be (as the first mover is said to be a principle) or with reference to the knowing of it.
762. But while all principles agree in the respect just mentioned, they nevertheless differ, because some are intrinsic and others extrinsic, as is clear from the above. Hence nature and element, which are intrinsic, can be principles-nature as that from which motion begins, and element as the first part in a thing's generation. "And mind," i.e., intellect, and "purpose," i.e., a man's intention, are said to be principles as extrinsic ones. Again, "a thing's substance," i.e., its form, which is its principle of being, is called an intrinsic principle, since a thing has being by its form. Again, according to what has been said, that for the sake of which something comes to be is said to be one of its principles. For the good, which has the character of an end in the case of pursuing, and evil in that of shunning, are principles of the knowledge and motion of many things; that is, all those which are done for the sake of some end. For in the realm of nature, in that of moral acts, and in that of artifacts, demonstrations make special use of the final cause.

LESSON 2
The Four Classes of Causes. Several Causes of the Same Effect. Causes May Be Causes of Each Other. Contraries Have the Same Cause
ARISTOTLE'S TEXT Chapter 2: 1013a 24-1013b 16
405. In one sense the term cause means that from which, as something intrinsic, a thing comes to be, as the bronze of a statue and the silver of a goblet, and the genera of these. In another sense it means the form and pattern of a thing, i.e., the intelligible expression of the quiddity and its genera (for example, the ratio of 2: 1 and number in general are the cause of an octave chord) and the parts which are included in the intelligible expression. Again, that from which the first beginning of change or of rest comes is a cause; for example, an adviser is a cause, and a father is the cause of a child, and in general a maker is a cause of the thing made, and a changer a cause of the thing changed. Further, a thing is a cause inasmuch as it is an end, i.e., that for the sake of which something is done; for example, health is the cause of walking. For if we are asked why someone took a walk, we answer, "in order to be healthy"; and in saying this we think we have given the cause. And whatever occurs on the way to the end under the motion of something else is also a cause. For example, reducing, purging, drugs and instruments are causes of health; for all of these exist for the sake of the end, although they differ from each other inasmuch as some are instruments and others are processes. These, then, are nearly all the ways in which causes are spoken of.
406. And since there are several senses in which causes are spoken of, it turns out that there are many causes of the same thing, and not in an accidental way. For example, both the maker of a statue and the bronze are causes of a statue not in any other respect but insofar as it is a statue. However, they are not causes in the same way, but the one as matter and the other as the source of motion.
407. And there are things which are causes of each other. Pain, for example, is a cause of health, and health is a cause of pain, although not in the same way, but one as an end and the other as a source of motion.
408. Further, the same thing is sometimes the cause of contraries; for that which when present is the cause of some particular thing, this when absent we sometimes blame for the contrary. Thus the cause of the loss of a ship is the absence of the pilot whose presence is the cause of the ship's safety. And both of these—the absence and the presence—are moving causes.
COMMENTARY
The four causes
763. Here the Philosopher distinguishes the various senses in which the term cause is used; and in regard to this he does two things. First, he enumerates the classes of causes. Second (783), he gives the modes of causes (“Now the modes”).
In regard to the first part he does two things. First, he enumerates the various classes of causes. Second (777), he reduces them to four (“All the causes”).
In regard to the first part he does two things. First, he enumerates the different classes of causes. Second (773), he clarifies certain things about the classes of causes (“And since”).
He accordingly says, first, that in one sense the term cause means that from which a thing comes to be and is “something intrinsic,” i.e., something which exists within the thing. This is said to distinguish it from a privation and also from a contrary; for a thing is said to come from a privation or from a contrary as from something which is not intrinsic; for example, white is said to come from black or from not-white. But a statue comes from bronze and a goblet from silver as from something which is intrinsic; for the nature bronze is not destroyed when a statue comes into being, nor is the nature silver destroyed when a goblet comes into being. Therefore the bronze of a statue and the silver of a goblet are causes in the sense of matter. He adds “and the genera of these,” because if matter is the species of anything it is also its genus. For example, if the matter of a statue is bronze, its matter will also be metal, compound and body. The same holds true of other things.
764. In another sense cause means the form and pattern of a thing, i.e., its exemplar. This is the formal cause, which is related to a thing in two ways. (1) In one way it stands as the intrinsic form of a thing, and in this respect it is called the formal principle of a thing. (2) In another way it stands as something which is extrinsic to a thing but is that in likeness to which it is made, and in this respect an exemplar is also called a thing’s form. It is in this sense that Plato held the Ideas to be forms. Moreover, because it is from its form that each thing derives its nature, whether of its genus or of its species, and the nature of its genus or of its species is what is signified by the definition, which expresses its quiddity, the form of a thing is therefore the intelligible expression of its quiddity, i.e., the formula by which its quiddity is known. For even though certain material parts are given in the definition, still it is from a thing’s form that the principal part of the definition comes. The reason why the form is a cause, then, is that it completes the intelligible expression of a thing’s quiddity. And just as the genus of a particular matter is also matter, in a similar way the genera of forms are the forms of things; for example, the form of the octave chord is the ratio of 2:1. For when two notes stand to each other in the ratio of 2:1, the interval between them is one octave. Hence twoness is its form; for the ratio of 2:1 derives its meaning from twoness. And because number is the genus of twoness, we may therefore say in a general way that number is also the form of the octave, inasmuch as we may say that the octave chord involves the ratio of one number to another. And not only is the whole definition related to the thing defined as its form, but so also are the parts of the definition, i.e., those which are given directly in the definition. For just as two-footed animal capable of walking is the form of man, so also are animal, capable of walking and two-footed. But sometimes matter is given indirectly in the definition, as when the soul is said to be the actuality of a physical organic body having life potentially.
765. In a third sense cause means that from which the first beginning of change or of rest comes, i.e., a moving or efficient cause. He says “of change or of rest,” because motion and rest which are natural are traced back to the same cause, and the same is true of motion and of rest which are a result of force. For that cause by which something is moved to a place is the same as that by which it is made to rest there. “An adviser” is an example of this kind of cause, for it is as a result of an adviser that motion begins in the one who acts upon his advice for the sake of safeguarding something. And in a similar way “a father is the cause of a child.” In these two examples Aristotle touches upon the, two principles of motion from which all things come to be, namely, purpose in the case of an adviser, and nature in the case of a father. And in general every maker is a cause of the thing made and every changer a cause of the thing changed.
766. Moreover, it should be noted that according to Avicenna, there are four modes of efficient cause, namely, perfective, dispositive, auxiliary and advisory.
An efficient cause is said to be perfective inasmuch as it causes the final perfection of a thing, as the one who induces a substantial form in natural things or artificial forms in things made by art, as a builder induces the form of a house.
767. An efficient cause is said to be dispositive if it does not induce the final form that perfects a thing but only prepares the matter for that form, as one who hews timbers and stones is said to build a house. This cause is not properly said to be the efficient cause of a house, because what he produces is only potentially a house. But he will be more properly an efficient cause if he induces the ultimate disposition on which the form necessarily follows; for example, man generates man without causing his intellect, which comes from an extrinsic cause.
768. And an efficient cause is said to be auxiliary insofar as it contributes to the principal effect. Yet it differs from the principal efficient cause in that the principal efficient cause acts for its own end, whereas an auxiliary cause acts for an end which is not its own. For example, one who assists a king in war acts for the king’s end. And this is the way in which a secondary cause is disposed for a primary cause. For in the case of all efficient causes which are directly subordinated to each other, a secondary cause acts because of the end of a primary cause; for example, the military art acts because of the end of the political art.
769. And an advisory cause differs from a principal efficient cause inasmuch as it specifies the end and form of the activity. This is the way in which the first agent acting by intellect is related to every secondary agent, whether it be natural or intellectual. For in every case a first intellectual agent gives to a secondary agent its end and its form of activity; for example, the naval architect gives these to the shipwright, and the first intelligence does the same thing for everything in the natural world.
770. Further, to this genus of cause is reduced everything that makes anything to be in any manner whatsoever, not only as regards substantial being, but also as regards accidental being, which occurs in every kind of motion. Hence he says not only that the maker is the cause of the thing made, but also that the changer is the cause of the thing changed.
771. In a fourth sense cause means a thing’s end, i.e., that for the sake of which something is done, as health is the cause of walking. And since it is less evident that the end is a cause in view of the fact that it comes into being last of all (which is also the reason why this cause was overlooked by the earlier philosophers, as was pointed out in Book I (1771), he therefore gives a special proof that an end is a cause. For to ask why or for what reason is to ask about a cause, because when we are asked why or for what reason someone walks, we reply properly by answering that he does so in order to be healthy. And when we answer in this way we think that we are stating the cause. Hence it is evident that the end is a cause. Moreover, not only the ultimate reason for which an agent acts is said to be an end with respect to those things which precede it, but everything that is intermediate between the first agent and the ultimate end is also said to be an end with respect to the preceding agents. And similarly those things are said to be causes from which motion arises in subsequent things. For example, between the art of medicine, which is the first efficient cause in this order, and health, which is the ultimate end, there are these intermediates: reducing, which is the most proximate cause of health in those who have a superfluity of humors; purging, by means of which reducing is brought about; “drugs,” i.e., laxative medicine, by means of which purging is accomplished; and “instruments,” i.e., the instruments by which medicine or drugs are prepared and administered. And all such things exist for the sake of the end, although one of them is the end of another. For reducing is the end of purging, and purging is the end of purgatives. However, these intermediates differ from each other in that (1) some are instruments, i.e., the instruments by means of which medicine is prepared and administered (and the administered medicine itself is something which nature employs as an instrument); and (2) some—purging and reducing—are processes, i.e., operations or activities.
772. He concludes, then, that “these are the ways in which causes are spoken of (405),” i.e., the four ways; and he adds “nearly all” because of the modes of causes which he gives below. Or he also adds this because the same classes of causes are not found for the same reason in all things.
773. And since (406).
Then he indicates certain points which follow from the things said above about the causes, and there are four of these. The first is that, since the term cause is used in many senses, there may be several causes of one thing not accidentally but properly. For the fact that there are many causes of one thing accidentally presents no difficulty, because many things may be accidents of something that is the proper cause of some effect, and all of these can be said to be accidental causes of that effect. But that there are several proper causes of one thing becomes evident from the fact that causes are spoken of in various ways. For the maker of a statue is a proper cause and not an accidental cause of a statue, and so also is the bronze, but not in the same way. For it is impossible that there should be many proper causes of the same thing within the same genus and in the same order, although there can be many causes providing that (1) one is proximate and another remote; or (2) that neither of them is of itself a sufficient cause, but both together. An example would be many men rowing a boat. Now in the case in point these two things are causes of a statue in different ways: the bronze as matter, and the artist as efficient cause.
774. And there are (407).
Then he sets down the second fact that may be drawn from the foregoing discussion. He says that it may also happen that any two things may be the cause of each other, although this is impossible in the same class of cause. But it is evident that this may happen when causes are spoken of in different senses. For example, the pain resulting from a wound is a cause of health as an efficient cause or source of motion, whereas health is the cause of pain as an end. For it is impossible, that a thing should be both a cause and something caused. Another text states this better, saying that “exercise is the cause of physical fitness,” i.e., of the good disposition caused by moderate exercise, which promotes digestion and uses up superfluous humors.
775. Now it must be borne in mind that, although four causes are given above, two of these are related to one another, and so also are the other two. (1) The efficient cause is related to the final cause, and (2) the material cause is related to the formal cause. The efficient cause is related to the final cause because the efficient cause is the starting point of motion and the final cause is its terminus. There is a similar relationship between matter and form. For form gives being, and matter receives it. Hence the efficient cause is the cause of the final cause, and the final cause is the cause of the efficient cause. The efficient cause is the cause of the final cause inasmuch as it makes the final cause be, because by causing motion the efficient cause brings about the final cause. But the final cause is the cause of the efficient cause, not in the sense that it makes it be, but inasmuch as it is the reason for the causality of the efficient cause. For an efficient cause is a cause inasmuch as it acts, and it acts only because of the final cause. Hence the efficient cause derives its causality from the final cause. And form and matter are mutual causes of being: form is a cause of matter inasmuch as it gives actual being to matter, and matter is a cause of form inasmuch as it supports form in being. And I say that both of these together are causes of being either in an unqualified sense or with some qualification. For substantial form gives being absolutely to matter, whereas accidental form, inasmuch as it is a form, gives being in a qualified sense. And matter sometimes does not support a form in being in an unqualified sense but according as it is the form of this particular thing and has being in this particular thing. This is what happens in the case of the human body in relation to the rational soul.
776. Further, the same thing (408).
Then he gives the third conclusion that may be drawn from the foregoing discussion. He says that the same thing can be the cause of contraries. This would also seem to be difficult or impossible if it were related to both in the same way. But it is the cause of each in a different way. For that which when present is the cause of some particular thing, this when absent “we blame,” i.e., we hold it responsible, “for the contrary.” For example, it is evident that by his presence the pilot is the cause of a ship’s safety, and we say that his absence is the cause of the ship’s loss. And lest someone might think that this is to be attributed to different classes of causes, just as the preceding two were, he therefore adds that both of these may be reduced to the same class of cause—the moving cause. For the opposite of a cause is the cause of an opposite effect in the same line of causality as that in which the original cause was the cause of its effect.

LESSON 3
All Causes Reduced to Four Classes
ARISTOTLE'S TEXT Chapter 2: 1013b 16-1014a 25
409. All the causes mentioned fall under one of the four classes which are most evident. For the elements of syllables, the matter of things made by art, fire and earth and all such elements of bodies, the parts of a whole, and the premises of a conclusion, are all causes in the sense of that from which things are made. But of these some are causes as a subject, for example, parts, and others as the essence, for example, the whole, the composition and the species, whereas the seed, the physician, the adviser, and in general every agent, are all sources of change or of rest. But the others are causes as the end and the good of other things. For that for the sake of which other things come to be is the greatest good and the end of other things. And it makes no difference whether we say that it is a good or an apparent good. These, then, are the causes, and this the number of their classes.
410. Now the modes of causes are many in number, but these become fewer when summarized. For causes are spoken of in many senses; and of those which belong to the same class, some are prior and some subsequent. For example, both the physician and one possessing an art are causes of health, and both the ratio of 2:1 and number are causes of the octave chord; and always those classes which contain singulars. Further, a thing may be a cause in the sense of an accident, and the classes which contain these; for example, in one sense the cause of a statue is Polyclitus and in another a sculptor, because it is accidental that a sculptor should be Polyclitus. And the universals which contain accidents are causes; for example, man is the cause of a statue, and even generally animal, because Polyclitus is a man and an animal. And of accidental causes some are more remote and some more proximate than others. Thus what is white and what is musical might be said to be the causes of a statue, and not just Polyclitus or man. Again, in addition to all of these, i.e., both proper causes and accidental causes, some are said to be causes potentially and some actually, as a builder and one who is building. And the distinctions which have been made will apply in like manner to the effects of these causes, for example, to this statue, or to a statue, or to an image generally, or to this bronze, or to bronze, or to matter in general. And the same applies to accidental effects. Again, both proper and accidental causes may be spoken of together, so that the cause of a statue may be referred to as neither Polyclitus nor a sculptor but the sculptor Polyclitus. But while all these varieties of causes are six in number, each is spoken of in two ways; for causes are either singular or generic; either proper or accidental, or generically accidental; or they are spoken of in combination or singly; and again they are either active or potential causes. But they differ in this respect, that active causes, i.e. singular causes, exist or cease to exist simultaneously with their effects, as this particular one who is healing with this particular person who is being healed, and as this particular builder with this particular thing which is being built. But this is not always true of potential causes; for the builder and the thing built do not cease to exist at the same time.
COMMENTARY
Four modes of causes
777. Here the philosopher reduces all causes to the classes of causes mentioned above (409), saying that all those things which are called causes fall into one of the four classes mentioned above. For “elements,” i.e., letters, are said to be the causes of syllables; and the matter of artificial things is said to be their cause; and fire and earth and all simple bodies of this kind are said to be the causes of compounds. And parts are said to be the causes of a whole, and “premises,” i.e., propositions previously set down from which conclusions are drawn, are said to be the causes of the conclusion. And in all of these cases cause has a single formal aspect according as cause means that from which a thing is produced, and this is the formal aspect of material cause.
778. Now it must be noted that propositions are said to constitute the matter of a conclusion, not inasmuch as they exist under such a form, or according to their force (for in this way they would rather have the formal aspect of an efficient cause), but with reference to the terms of which they are composed. For a conclusion is constituted of the terms contained in the premises, i.e., of the major and minor terms.
779. And of those things of which something is composed, some are like a subject, for example, parts and the other things mentioned above, whereas some are like the essence, for example, the whole, the composition and the species, which have the character of a form whereby a thing’s essence is made complete. For it must be borne in mind that (1) sometimes one thing is the matter of something else in an unqualified sense (for example, silver of a goblet), and then the form corresponding to such a matter can be called the species. (2) But sometimes many things taken together constitute the matter of a thing; and this may occur in three ways. (a) For sometimes things are united merely by their arrangement, as the men in an army or the houses in a city; and then the whole has the role of a form which is designated by the term army or city. (b) And sometimes things are united not just by arrangement alone but by contact and a bond, as is evident in the parts of a house; and then their composition has the role of a form. (c) And sometimes the alteration of the component parts is added to the above, as occurs in the case of a compound; and then the compound state itself is the form, and this is still a kind of composition. And a thing’s essence is derived from any one of these three—the composition’ species, or whole—as becomes clear when an army, a house, or a goblet is defined. Thus we have two classes of cause.
780. But the seed, the physician and the adviser, and in general every agent, are called causes for a different reason, namely, because they are the sources of motion and rest. Hence this is now a different class of cause because of a different formal aspect of causality. He puts seed in this class of cause because he is of the opinion that the seed has active power, whereas a woman’s menstrual fluid has the role of the matter of the offspring.
781. There is a fourth formal aspect of causality inasmuch as some things are said to be causes in the sense of the end and good of other things. For that for the sake of which something else comes to be is the greatest good “and the end” of other things, i.e., it is naturally disposed to be their end. But because someone could raise the objection that an end is not always a good since certain agents sometimes inordinately set up an evil as their end, he therefore replies that it makes no difference to his thesis whether we speak of what is good without qualification or of an apparent good. For one who acts does so, properly speaking, because of a good, for this is what he has in mind. And one acts for the sake of an evil accidentally inasmuch as he happens to think that it is good. For no one acts for the sake of something with evil in view.
782. Moreover, it must be noted that, even though the end is the last thing to come into being in some cases, it is always prior in causality. Hence it is called the “cause of causes”, because it is the cause of the causality of all causes. For it is the cause of efficient causality, as has already been pointed out (775); and the efficient cause is the cause of the causality of both the matter and the form, because by its motion it causes matter to be receptive of form and makes form exist in matter. Therefore the final cause is also the cause of the causality of both the matter and the form. Hence in those cases in which something is done for an end (as occurs in the realm of natural things, in that of moral matters, and in that of art), the most forceful demonstrations are derived from the final cause. Therefore he concludes that the foregoing are causes, and that causes are distinguished into this number of classes.
783. Now the modes (410).
Then he distinguishes between the modes of causes. And causes are distinguished into classes and into modes. For the division of causes into classes is based on different formal aspects of causality, and is therefore equivalently a division based on essential differences, which constitute species. But the division of causes into modes is based on the different relationships between causes and things caused, and therefore pertains to those causes which have the same formal aspect of causality. An example of this is the division of causes into proper and accidental causes, and into remote and proximate causes. Therefore this division is equivalently a division based on accidental differences, which do not constitute different species.
784. He accordingly says that there are many modes of causes, but that these are found to be fewer in number when “summarized,” i.e., when brought together under one head. For even though proper causes and accidental causes are two modes, they are still reduced to one head insofar as both may be considered from the same point of view. The same thing is true of the other different modes. For many different modes of causes are spoken of, not only with reference to the different species of causes, but also with reference to causes of the same species, namely, those which are reduced to one class of cause.
785. (1) For one cause is said to be prior and another subsequent; and causes are prior or subsequent in two ways: (1) In one way, when there are many distinct causes which are related to each other, one of which is primary and remote, and another secondary and proximate (as in the case of efficient causes man generates man as a proximate and subsequent cause, but the sun as a prior and remote cause); and the same thing can be considered in the case of the other classes of causes. (2) In another way, when the cause is numerically one and the same, but is considered according to the sequence which reason sets up between the universal and the particular; for the universal is naturally prior and the particular subsequent.
786. But he omits the first way and considers the second. For in the second way the effect is the immediate result of both causes, i.e., of both the prior and subsequent cause; but this cannot happen in the first way. Hence he says that the cause of health is both the physician and one possessing an art, who belong to the class of efficient cause: one possessing an art as a universal and prior cause, and the physician as a particular, or special, and subsequent cause. The same thing is true of the formal cause, since this cause may also be considered in two ways; for example, for an octave chord “double,” or the ratio of 2:1, or the number two, is a formal cause as one that is special and subsequent, whereas number, or the ratio of one number to another or to the unit, is like a universal and prior cause. And in this way too “always those classes which contain singulars,” i.e., universals, are said to be prior causes.
787. (2) Causes are distinguished in another way inasmuch as one thing is said to be a proper cause and another an accidental cause. For just as proper causes are divided into universal and particular, or into prior and subsequent, so also are accidental causes. Therefore, not only accidental causes themselves are called such, but so also are the classes which contain these. For example, a sculptor is the proper cause of a statue, and Polyclitus is an accidental cause inasmuch as he happens to be a sculptor. And just as Polyclitus is an accidental cause of a statue, in a similar way all universals “which contain accidents,” i.e., accidental causes, are said to be accidental causes, for example, man and animal, which contain under themselves Polyclitus, who is a man and an animal.
788. And just as some proper causes are proximate and some remote, as was pointed out above, so also is this the case with accidental causes. For Polyclitus is a more proximate cause of a statue than what is white or what is musical. For an accidental mode of predication is more remote when an accident is predicated of an accident than when an accident is predicated of a subject. For one accident is predicated of another only because both are predicated of a subject. Hence when something pertaining to one accident is predicated of another, as when something pertaining to a builder is predicated of a musician, this mode of predication is more remote than one in which something is predicated of the subject of an accident, as when something pertaining to a builder is predicated of Polyclitus.
789. Now it must be borne in mind that one thing can be said to be the accidental cause of something else in two ways: (1) in one way, from the viewpoint of the cause; because whatever is accidental to a cause is itself called an accidental cause, for example, when we say that something white is the cause of a house. (2) In another way, from the viewpoint of the effect, i.e., inasmuch as one thing is said to be an accidental cause of something else because it is accidental to the proper effect. This can happen in three ways:
The first is that the thing has a necessary connection with the effect. Thus that which removes an obstacle is said to be a mover accidentally. This is the case whether that accident is a contrary, as when bile prevents coolness (and thus scammony is said to produce coolness accidentally, not because it causes coolness, but because it removes the obstacle preventing coolness, i.e., bile, which is its contrary); or even if it is not a contrary, as when a pillar hinders the movement of a stone which rests upon it, so that one who removes the pillar is said to move the stone accidentally.
In a second way, something is accidental to the proper effect when the accident is connected with the effect neither necessarily nor in the majority of cases but seldom, as the discovery of a treasure is connected with digging in the soil. It is in this way that fortune and chance are said to be accidental causes.
In a third way things are accidental to the effect when they have no connection except perhaps in the mind, as when someone says that he is the cause of an earthquake because an earthquake took place when he entered the house.
790. [Cross-division of all] And besides the distinction of all things into causes in themselves or proper causes and accidental causes, there is a third division of causes inasmuch as some things are causes potentially and some actually, i.e., actively. For example, the cause of building is a builder in a state of potency (for this designates his habit or office), or one who is actually building.
791. And the same distinctions which apply to causes can apply to the effects of which these causes are the causes. For effects, whether particular or universal, can be divided into prior and subsequent, as a sculptor may be called the cause of this statue, which is subsequent; or of a statue, which is more universal and prior; or of an image, which is still more universal. And similarly something is the formal cause of this particular bronze; or of bronze, which is more universal; or of matter, which is still more universal. The same things can be said of accidental effects, i.e., of things produced by accident. For a sculptor who is the cause of a statue is also the cause of the heaviness, whiteness or redness which are in it as accidents from the matter and are not caused by this agent.
792. (3) Again, he gives a fourth division of causes, namely, the division into simple causes and composite causes. A cause is said to be simple (a) when, for example, in the case of a statue, the proper cause alone is considered, as a sculptor, or when an accidental cause alone is considered, as Polyclitus. But a cause is said to be composite when both are taken together, for example, when we say that the cause of a statue is the sculptor Polyclitus.
793. (b) There is moreover another way in which causes are said to be composite, i.e., when several causes act together to produce one effect, for example, when many men act together in order to row a boat, or when many stones combine in order to constitute the matter of a house. But he omits the latter way because no one of these things taken in itself is the cause, but a part of the cause.
794. And having given these different modes of causes, he brings out their number, saying that these modes of causes are six in number, and that each of these have two alternatives so that twelve result. For these six modes are (1-2) either singular or generic (or, as he called them above, prior and subsequent); (3-4) either proper or accidental (to which the genus of the accident is also reduced, for the genus to which an accident belongs is an accidental cause); and again, (5-6) either composite or simple. Now these six modes are further divided by potency and actuality and thus are twelve in number. Now the reason why all these modes must be divided by potency and actuality is that potency and actuality distinguish the connection between cause and effect. For active causes are at one and the same time particulars and cease to exist along with their effects; for example, this act of healing ceases with this act of recovering health, and this act of building with this thing being built; for a thing cannot be actually being built unless something is actually building. But potential causes do not always cease to exist when their effects cease; for example, a house and a builder do not cease to exist at one and the same time. In some cases, however, it does happen that when the activity of the efficient cause ceases the substance of the effect ceases. This occurs in the case of those things whose being consists in coming to be, or whose cause is not only the cause of their coming to be but also of their being. For example, when the sun’s illumination is removed from the atmosphere, light ceases to be. He says “singular causes” because acts belong to singular things, as was stated in Book I of this work (21).

LESSON 4
The Proper Meaning of Element; Elements in Words, Natural Bodies, and Demonstrations. Transferred Usages of "Element" and Their Common Basis
ARISTOTLE'S TEXT Chapter 3: 1014a 25-1014b 15
411. The inherent principle of which a thing is first composed and which is not divisible into another species is called an element. For example, the elements of a word are the parts of which a word is composed and into which it is ultimately divided and which are not further divided into other words specifically different from them. But if they are divided, their parts are alike, as the parts of water are water; but this is not true of the syllable. Similarly, people who speak of the elements of bodies mean the component parts into which bodies are ultimately divided and which are not divided into other bodies specifically different. And whether such parts are one or many, they call them elements. And similarly the parts of diagrams are called elements, and in general the parts of demonstrations; for the primary demonstrations which are contained in many other demonstrations are called the elements of demonstrations; and such are the primary syllogisms which are composed of three terms and proceed through one middle term.
412. People also use the term element in a transferred sense of anything which is one and small and useful for many purposes; and for this reason anything which is small and simple and indivisible is called an element. Hence it follows that the most universal things are elements, because each of them, being one and simple, is found in many things, either in all or in most of them. And to some the unit and the point seem to be principles. Therefore, since what are called genera are universal and indivisible (for their formal character is one), some men call the genera elements, and these more than a difference, since a genus is more universal. For where the difference is present the genus also follows, but the difference is not always present where the genus is. And in all these cases it is common for the element of each thing to be the primary component of each thing.
COMMENTARY
Element
795. Here he distinguishes the different senses of the term element, and in regard to this lie does two things. First, he gives the different senses in which the term element is used. Second (807), he indicates what all of them have in common (“And in all these”).
In regard to the first he does two things. First, he explains how the term element is used in its proper sense; and second (802), how it is used in transferred senses (“People also use”).
First, he gives a sort of description of an element, and from this one can gather the four notes contained in its definition. The first is that an element is a cause in the sense of that from which a thing comes to be; and from this it is clear that an element is placed in the class of material cause.
796. The second is that an element is the principle from which something first comes to be. For copper is that from which a statue comes to be, but it is still not an element because it has some matter from which it comes to be.
797. The third is that an element is inherent or intrinsic; and for this reason. it differs from everything of a transitory nature from which a thing comes to be, whether it be a privation or a contrary or the matter subject to contrariety and privation, which is transitory; for example, when we say that a musical man comes from a nonmusical man, or that the musical comes from the non-musical. For elements must remain in the things of which they are the elements.
798. The fourth is that an element has a species which is not divisible into different species; and thus an element differs from first matter, which has no species, and also from every sort of matter which is capable of being divided into different species, as blood and things of this kind.
Hence he says, as the first note, that an element is that of which a thing is composed; as the second, that it is that of which a thing is “first” composed; as the third, that it is “an inherent principle”; and as the fourth, that it is “not divisible into another species.”
799. He illustrates this definition of element in four cases in which we use the term element. For we say that letters are the elements of a word because every word is composed of them, and of them primarily. This is evident from the fact that all words are divided into letters as ultimate things; for what is last in the process of dissolution must be first in the process of composition. But letters are not further divided into other words which are specifically different. Yet if they should be divided in any way, the parts in which the division results would be “alike,” i.e., specifically the same, just as all parts of water are water. Now letters are divided according to the amount of time required to pronounce them, inasmuch as a long letter is said to require two periods of time, and a short letter one. But while the parts into which letters are so divided do not differ as the species of words do, this is not the case with a syllable; for its parts are specifically different, since the sounds which a vowel and a consonant make, of which a syllable is composed, are specifically different.
800. He gives as a second example natural bodies, certain of which we also call the elements of certain others. For those things into which all compounds are ultimately dissolved are called their elements; and therefore they are the things of which bodies of this kind are composed. But those bodies which are called elements are not divisible into other bodies which are specifically different, but into like parts, as any part of water is water. And all those who held for one such body into which every body is dissolved and which is itself incapable of being further divided, said that there is one element. Some said that it is water, some air, and some fire. But those who posited many such bodies also said there are many elements. Now it should be borne in mind that when it is set down in the definition of an element that an element is not divisible into different species, this should not be understood of the parts into which a thing is divided in a quantitative division (for wood would then be an element, since any part of wood is wood), but in a division made by alteration, as compounds are dissolved into simple bodies.
801. As a third example he gives the order of demonstrations, in which we also employ the word element; for example, we speak of Euclid’s Book of Elements. And he says that, in a way similar and close to those mentioned, those things which “are parts of diagrams,” i.e., the constituents of geometrical figures, are called elements. This can be said not only of the demonstrations in geometry but universally of all demonstrations. For those demonstrations which have only three terms are called the elements of other demonstrations, because the others are composed of them and resolved into them. This is shown as follows: a second demonstration takes as its starting point the conclusion of a first demonstration, whose terms are understood to contain the middle term which was the starting point of the first demonstration. Thus the second demonstration will proceed from four terms the first from three only, the third from five, and the fourth from six; so that each demonstration adds one term. Thus it is clear that first demonstrations are included in subsequent ones, as when this first demonstration—every B is A, every C is B, therefore every C is A—is included in this demonstration—every C is A, every D is C, therefore every D is A; and this again is included in the demonstration whose conclusion is that every E is A, so that for this final conclusion there seems to be one syllogism composed of several syllogisms having several middle terms. This may be expressed thus: every B is A, every C is B, every D is C, every E is D, therefore every E is A. Hence a first demonstration, which has one middle term and only three terms, is simple and not reducible to another demonstration, whereas all other demonstrations are reducible to it. Hence first syllogisms, which come from three terms by way of one middle term, are called elements.
802. People also use (412).
Here he shows how the term element is used in a transferred sense. He says that some men, on the basis of the foregoing notion or meaning of element, have used the term in a transferred sense to signify anything that is one and small and useful for many purposes. For from the fact that an element is indivisible they understood that it is one; and from the fact that it is first they understood that it is simple; and from the fact that other things are composed of elements they understood that an element is useful for many purposes. Hence they set up this definition of an element in order that they might say that everything which is smallest in quantity and simple (inasmuch as it is not composed of other things) and incapable of division into different species, is an element.
803. But when they had set up this definition of element, it turned out that by using it in a transferred sense they had invented two senses of element. First, they called the most universal things elements; for a universal is one in definition and is simple (because its definition is not composed of different parts) and is found in many things, and thus is useful for many purposes, whether it be found in all things, as unity and being are, or in most things, as the other genera. And by the same reasoning it came about, second, that they called points and units principles or elements because each of them is one simple thing and useful for many purposes.
804. But in this respect they fell short of the true notion of a principle, because universals are not the matter of which particular things are composed but predicate their very substance. And similarly points are not the matter of a line, for a line is not composed of points.
805. Now with this transferred notion of element established, the solution to a question disputed in Book III (431-36) becomes clear, i.e., whether a genus or a species is more an element, and whether a genus or a difference is more an element; for it clearly follows that genera are elements to a greater degree because genera are more universal and indivisible. For there is no concept or definition of them which must be composed of genera and differences, but it is species which are properly defined. And if a genus is defined, it is not defined insofar as it is a genus but insofar as it is a species. Hence a species is divided into different parts and thus does not have the character of an element. But a genus is not divisible into different parts, and therefore they said that genera are elements more than species. Another translation reads, “For their formal character is one,” that is, indivisible, because even though genera do not have a definition, still what is signified by the term genus is a simple conception of the intellect which can be called a definition.
806. And just as a genus is more an element than a species is because it is simpler, in a similar way it is more an element than a difference is, even though a difference is simple, because a genus is more universal. This is clear from the fact that anything which has a difference has a genus, since essential differences do not transcend a genus; but not everything which has a genus necessarily has a difference.
807. Last of all he says that all of the foregoing senses of element have this note in common, that an element is the primary component of each being, as has been stated.

LESSON 5
Five Senses of the Term Nature
ARISTOTLE'S TEXT Chapter 4: 1014b 15-1015a 20
413. Nature means, in one sense, the generation of things that are born, as if one were to pronounce the letter u [in fusij ] long. And in another sense it means the immanent principle from which anything generated is first produced. Again, it means the source of the primary motion in any beings which are by nature, and it is in each inasmuch as it is such. Now all those things are said to be born which increase through something else by touching and by existing together, or by being naturally joined, as in the case of embryos. But being born together differs from touching, for in the latter case there need be nothing but contact. But in things which are naturally joined together there is some one same thing in both, instead of contact, which causes them to be one, and which makes them to be one in quantity and continuity but not in quality. Again, nature means the primary thing of which a natural being is composed or from which it comes to be, when it is unformed and immutable by its own power; for example, the bronze of a statue or of bronze articles is said to be their nature, and the wood of wooden things, and the same applies in the case of other things. For each thing comes from these though its primary matter is preserved. For it is also in this sense that men speak of the elements of natural beings as their nature; some calling it fire, others earth, others water, others air, and others something similar to these, whereas others call all of them nature. In still another sense nature means the substance of things which are by nature, as those who say that nature is the primary composition of a thing, as Empedocles says, "Of nothing that exists is there nature, but only the mixing and separating-out of what has been mixed. Nature is but the name men give to these. For this reason we do not say that things which are or come to be by nature have a nature, even when that from which they can be or come to be is already present, so long as they do not have their form or species. Hence that which is composed of both of these exists by nature, as animals and their parts.
414. Again, nature is the primary matter of a thing, and this in two senses: either what is primary with respect to this particular thing, or primary in general; for example, the primary matter of bronze articles is bronze, but in general it is perhaps water, if everything capable of being liquefied is water. And nature is also a thing's form or substance, i.e., the terminus of the process of generation. But metaphorically speaking every substance in general is called nature because of form or species, for the nature of a thing is also a kind of substance.
415. Hence, from what has been said, in its primary and proper sense nature is the substance of those things which have within themselves as such the source of their motion. For matter is called nature because it is receptive of this. And processes of generation and growth are called nature because they are motions proceeding from it. And nature is the source of motion in those things which are by nature, and it is something present in them either potentially or in complete actuality.
COMMENTARY
Nature
808. Here he gives the different meanings of the term nature. And even though an investigation of the term nature appears not to belong to first philosophy but rather to the philosophy of nature, he nevertheless gives the different meanings of this term here, because according to one of its common meanings nature is predicated of every substance, as he will make clear. Hence it falls under the consideration of first philosophy just as universal substance does.
In regard to the first he does two things. First (808), he distinguishes the different senses in which the term nature is used. Second (824), he reduces all of these to one primary notion (“Hence, from what”).
In regard to the first he does two things. First, he gives five principal senses in which the term, nature is used. Second (821), he gives two additional senses connected with the last two of these (“Again, nature”).
(1) He accordingly says, first, that in one sense nature means the process of generation of things that are generated, or, according to another text which states this in a better way, “of things that are born.” For not everything that is generated can be said to be born but only living things, for example, plants and animals and their parts. The generation of non-living things cannot be called nature, properly speaking, according to the common use of the term, but only the generation of living things inasmuch as nature may mean the nativity or birth of a thing... Yet even from this text it can be understood that the term nature means the generation of living things by a certain lengthening or extension of usage.
809. Again, from the fact that nature was first used to designate the birth of a thing there followed a second use of the term, so that nature came to mean the principle of generation from which a thing comes to be, or that from which as from an intrinsic principle something born is first generated.
810. And as a result of the likeness between birth and other kinds of motion the meaning of the term nature has been extended farther, so that in a third sense it means the source from which motion begins in any being according to its nature, provided that it is present in it insofar as it is such a being and not accidentally. For example, the principle of health, which is the medical art, is not present in a physician who is ill insofar as he is ill but insofar as he is a physician. And he is not healed insofar as he is a physician but insofar as he is ill; and thus the source of motion is not in him insofar as he is moved. This is the definition of nature given in Book II of the Physics.
811. And because he mentioned things that are born, he also shows what it means in the proper sense “to be born,” as another text says, and in place of which this text incorrectly says “to be generated.” For the generation of living things differs from that of non-living things, because a non-living thing is not generated by being joined or united to its generator, as fire is generated by fire and water by water. But the generation of a living thing comes about through some kind of union with the principle of generation. And because the addition of quantity to quantity causes increase, therefore in the generation of living things there seems to be a certain increase, as when a tree puts forth foliage and fruit. Hence he says that those things are said to be born which “increase,” i.e., have some increase together with the principle of generation [i.e. multiply].
812. But this kind of increase differs from that class of motion which is called increase [or augmentation ], by which things that are already born are moved or changed. For a thing that increases within itself does so because the part added passes over into the substance of that thing, as food passes over into the substance of the one nourished. But anything that is born is added to the thing from which it is born as something other and different, and not as something that passes over into its substance. Hence he says that it increases “through something distinct” or something else, as if to say that this increase comes about through the addition of something that is other or different.
813. But addition that brings about increase can be understood to take place in two ways: in one way, “by touching,” i.e., by contact alone; in another way, “by existing together,” i.e., by the fact that two things are produced together and naturally connected with each other, as the arms and sinews; “and by being joined,” i.e., by the fact that something is naturally adapted to something else already existing, as hair to the head and teeth to the gums. In place of this another text reads, more appropriately, “by being born together with,” and “by being connected with at birth.” Now in the generation of living things addition comes about not only by contact but also by a kind of joining together or natural connection, as is evident in the case of embryos, which are not only in contact in the womb, but are also bound to it at the beginning of their generation.
814. Further, he indicates the difference between these two, saying that “being fused,” i.e., being bound together, or “being connected at birth,” as another text says, differs from contact, because in the case of contact there need be nothing besides the things in contact which makes them one. But in the case of things which are bound together, whether naturally connected or born together and joined at birth, there must be some one thing “instead of contact,” i.e., in the place of contact, which causes them “to be naturally joined,” i.e., joined or bound together or born together. Moreover, it must be understood that the thing which causes them to be one makes them one in quantity and continuity but not in quality; because a bond does not alter the things bound from their own dispositions.
815. And from this it is evident that anything that is born is always connected with the thing from which it is born. Hence nature never means an extrinsic principle, but in every sense in which it is used it is taken to mean an intrinsic principle.
816. (4) And from this third meaning of nature there follows a fourth. For if the source of motion in natural bodies is called their nature, and it seemed to some that the principle of motion in natural bodies is matter, it was for this reason that matter came to be called nature, which is taken as a principle of a thing both as to its being and as to its becoming. And it is also considered to be without any form, and is not moved by itself but by something else. He accordingly says that nature is spoken of as that primary thing of which any being is composed or from which it comes to be.
817. He says this because matter is a principle both of being and of becoming. Hence he says that “it is without order,” i.e., form; and for this reason another text says “when it is unformed”; for in the case of some things their order (or arrangement) is regarded as their form, as in the case of an army or of a city. And for this reason he says that it is “immutable by its own power,” i.e., it cannot be moved by its own power but by that of a higher agent. For matter does not move itself to acquire a form but is moved by a higher and extrinsic agent. For instance, we might say that “bronze is the nature of a statue or of bronze vessels” or “wood of wooden,” as if such vessels were natural bodies. The same is true of everything else that is composed of or comes to be from matter; for each comes to be from its matter though this is preserved. But in the process of generation the dispositions of a form are not preserved; for when one form is introduced another is cast out. And for this reason it seemed to some thinkers that forms are accidents and that matter alone is substance and nature, as he points out in the Physics, Book II
818. They held this view because they considered the matter and form of natural bodies in the same way as they did the matter and form of things made by art, in which forms are merely accidents and matter alone is substance. It was in this sense that the philosophers of nature said that the elements are the matter of things which come to be by nature, i.e., water, air, or fire, or earth, which no philosopher has held to be the element of natural beings all by itself, although some of those who were not philosophers of nature did hold this, as was stated in Book I (134). And some philosophers, such as Parmenides, held that some of these are the elements and natures of things; others, such as Empedocles, held that all four are the elements of things; and still others, such as Heraclitus, held that something different is the element of things, for he claimed that vapor plays this role.
819. (5) Now because motion is caused in natural bodies by the form rather than by the matter, he therefore adds a fifth sense in which the term nature is used: that in which nature means the form of a thing. Hence in another sense nature means “the substance of things,” i.e., the form of things, which are by nature. It was in this sense that some said that the nature of things is the composition of mixed bodies, as Empedocles said that there is nothing absolute in the world, but that only the alteration or loosening (or mixing, according to another text) of what has been mixed is called nature by men. For they said that things composed of different mixtures have different natures.
820. Now they were led to hold that form is nature by this process of reasoning: whatever things exist or come to be by nature are not said to have a nature, even though the matter from which they are naturally disposed to be or to come to be is already present, unless they have a proper species and a form through which they acquire their species. Now the term species seems to be given in place of substantial form and the term form in place of figure, which is a natural result of the species and a sign of it. Hence, if form is nature, a thing cannot be said to have a nature unless it has a form. Therefore, that which is composed of matter and form “is said to be by nature,” i.e., according to nature, as animals and the parts of animals, such as flesh and bones and the like.
821. Again, nature (414).
Then he gives two meanings of nature which are connected with the last two preceding ones, and the first of these is added to the fourth sense of nature, in which it means the matter of a thing. And he says that not every kind of matter is said to be the nature of a thing but only first matter. This can be understood in two senses: either with reference to something generic, or with reference to something that is first absolutely or without qualification. For example, the first matter generically of artificial things produced from bronze is bronze; but their first matter without qualification is water; for all things which are liquefied by heat and solidified by cold have the character of water, as he says in Book IV of the Meteors.
822. He links up the second of these additional meanings with the fifth sense of nature mentioned above, according to which nature means form. And in this sense not only the form of a part (forma partis) is called nature but the species is the form of the whole (forma totius). For example, we might say that the nature of man is not only a soul but humanity and the substance signified by the definition. For it is from this point of view that Boethius says that the nature of a thing is the specific difference which informs each thing, because the specific difference is the principle that completes a thing’s substance and gives it its species. And just as form or matter is called nature because it is a principle of generation, which is the meaning of nature according to the original use of the term, in a similar way the species or substance of a thing is called its nature because it is the end of the process of generation. For the process of generation terminates in the species of the thing generated, which is a result of the union of matter and form.
823. And because of this every substance is called nature according to a kind of metaphorical and extended use of the term; for the nature which we spoke of as the terminus of generation is a substance. Thus every substance is similar to what we call nature. Boethius also gives this meaning of the term. Moreover, it is because of this meaning that the term nature is distinguished from other common terms. For it is common in this way just as substance also is.
824. Hence, from what (415).
Then he reduces all of the foregoing senses of the term nature to one common notion. But it must be noted that the reduction of the other senses to one primary sense can happen in two ways: in one way, with reference to the order which things have; and in another way, with reference to the order which is observed in giving names to things. For names are given to things according as we understand them, because names are signs of what we understand; and sometimes we understand prior things from subsequent ones. Hence something that is prior for us receives a name which subsequently fits the object of that name. And this is what happens in the present case; for since the forms and powers of things are known from their activities, the process of generation or birth of a thing is the first to receive the name of nature and the last is the form.
825. But with reference to the order which things have in reality the concept of nature primarily fits the form, because, as has been said (808), nothing is said to have a nature unless it has a form.
826. Hence from what has been said it is evident that “in its primary and proper sense nature is the substance,” i.e., the form, of those things which have within themselves as such the source of their motion. For matter is called nature because it is receptive of form; and processes of generation get the name of nature because they are motions proceeding from a form and terminating in further forms. And this, namely, the form, is the principle of motion in those things which are by nature, either potentially or actually. For a form is not always the cause of actual motion but sometimes only of potential motion, as when a natural motion is prevented by an external obstacle, or even when a natural action is prevented by a defect in the matter.

LESSON 6
Four Senses of the Term Necessary. Its First and Proper Sense. Immobile Things, though Necessary, Are Exempted from Force
ARISTOTLE'S TEXT Chapter 5: 1015a 20-1015b 15
416. Necessary means that without which, as a contributing cause, a thing cannot be or live; for example, breathing and food are necessary to an animal because it cannot exist without them.
417. And it also means that without which the good for man cannot be or come to be, and that without which one cannot get rid of or remain free of some evil; for example, the drinking of some drug is necessary in order that one may not be in distress, and sailing to Aegina is necessary in order that one may collect money.
418. Again, it means what applies force and force itself, and this is something which hinders and prevents, in opposition to desire and choice. For that which applies force is said to be necessary, and for this reason anything necessary is also said to be lamentable, as Evenus says, "For every necessary thing is mournful." And force is a kind of necessity, as Sophocles says, "But force compels me to do this." And necessity seems to be something blameless, and rightly so, for it is contrary to motion which stems from choice and from knowledge.
419. Again, we say that anything which cannot be otherwise is necessarily so.
420. And from this sense of the term necessary all the other senses are derived. For whatever is forced is said either to do or to undergo something necessary when it cannot do something according to its inclination as a result of force, as if there were some necessity by reason of which the thing could not be otherwise. The same thing applies to the contributing causes of life and of good. For when in the one case good, and in the other life or being, is impossible without certain contributing causes, these are necessary; and this cause is a kind of necessity.
421. Further, demonstration belongs to the class of necessary things, because whatever has been demonstrated in the strict sense cannot be otherwise. The reason for this is the principles, for the principles from which a syllogism proceeds cannot be otherwise.
422. Now of necessary things some have something else as the cause of their necessity and others do not, but it is because of them that other things are necessary. Hence what is necessary in the primary and proper sense is what is simple, for this cannot be in more ways than one. Therefore it cannot be in one state and in another; otherwise there would be more ways than one. If, then, there are any beings which are eternal and immobile, in them nothing forced or contrary to nature is found.
COMMENTARY
Necessary
827. Having distinguished the different senses of the terms which signify causes, the Philosopher now gives the different senses of a term which designates something pertaining to the notion of cause, i.e., the term necessary; for a cause is that from which something else follows of necessity. In regard to this he does two things. First, he distinguishes the different senses of the term necessary. Second (836), he reduces all of these to one primary sense (“And from this sense”).
In the first part he gives four senses in which the term necessary is used:
First, it means that without which a thing cannot be or live; and even when this is not the principal cause of a thing, it is still a contributing cause. Breathing, for example, is necessary to an animal which breathes, because it cannot live without this. And while breathing is not the [principal] cause of life, nonetheless it is still a contributing cause inasmuch as it helps to restore what is lost and prevents the total consumption of moisture, which is a cause of life. Hence things of this kind are said to be necessary because it is impossible for things to exist without them.
828. And it also means (417).
Then he gives a second sense in which things are said to be necessary. He says that in a second way those things are said to be necessary without which some good cannot be or come about, or some evil be avoided or expelled. For example, we say that “the drinking of some drug,” i.e., a laxative medicine, is necessary, not because an animal cannot live without it, but because it is required to expel something, namely, an evil, illness, or even to avoid it. For this is necessary “in order that one may not be in distress,” i.e., to avoid being ill. And similarly “sailing to Aegina,” i.e., to a definite place, is necessary, not because a man cannot exist without this, but because he cannot acquire some good, i.e., money, without doing this. Hence, such a voyage is said to be necessary in order to collect a sum of money.
829. Again, it means (418).
Here he gives a third sense in which things are said to be necessary. He says that anything which exerts force, and even force itself, is termed necessary. For force is said to be necessary, and one who is forced is said to do of necessity whatever he is compelled to do. He shows what is meant by something that exerts force both in the case of natural beings and in that of beings endowed with will. In natural beings there is a desire for or an inclination toward some end or goal, to which the will of a rational nature corresponds; and for this reason a natural inclination is itself called an appetite. For both of these, i.e., both the desire of a natural inclination and the intention of the will, can be hindered and prevented—hindered in carrying out a motion already begun, and prevented from initiating motion. Therefore, that is said to be forced “which is done in opposition to desire,” ‘ i.e., against the inclination of a natural being; and it is “something that hinders choice,” i.e., the end intended in executing a voluntary motion already begun, and also something that prevents it from beginning. Another text says, “and this is according to impetuousness,” i.e., according to impulse. For force is found when something is done through the impulse of an external agent and is opposed to the will and power of the subject. And that is forced which is done as a result of an impulse applying force.
830. Now from this definition of the forced he draws two conclusions. The first is that everything forced is sad or mournful. He proves this by using the statement of a certain poet or teacher, saying that everything which is necessary or forced is sad or lamentable; for force is a kind of necessity, as the poet Sophodes says: “Force,” i.e., necessity, “compelled me to do this.” For it has been said that force is something which hinders the will; and things which are opposed to the will cause sorrow, because sorrow has to do with things which happen to us against our will.
831. The second conclusion is that anything which is necessary is rightly said to be without blame or reproach. For it is said that necessity deserves forgiveness rather than blame; and this is true because we deserve to be blamed only for the things which we do voluntarily and for which we may also be reasonably rebuked. But the kind of necessity which pertains to force is opposed to the will and to reason, as has been stated (829); and thus it is more reasonable to say that things done by force are not subject to blame.
832. Again, we say (419).
He gives a fourth sense in which things are said to be necessary. He says that being in such a state that it cannot be otherwise we also call necessary, and this is what is necessary in an absolute sense. Things necessary in the first senses, however, are necessary in a relative sense.
833. Now whatever is absolutely necessary differs from the other types of necessity, because absolute necessity belongs to a thing by reason of something that is intimately and closely connected with it, whether it be the form or the matter or the very essence of a thing. For example, we say that an animal is necessarily corruptible because this is a natural result of its matter inasmuch as it is composed of contraries; and we say that an animal is necessarily capable of sensing because this is a result of its form; and we also say that an animal is necessarily a living sensible substance because this is its essence.
834. However, the necessity of something which is necessary in a relative sense and not absolutely depends on an extrinsic cause. And there are two kinds of extrinsic causes—the end and the agent. The end is either existence taken absolutely, and the necessity taken from this end pertains to the first kind; or it is well disposed existence or the possession of some good, and necessity of the second kind is taken from this end.
835. Again, the necessity which comes from an external agent pertains to the third kind of necessity. For force exists when a thing is moved by an external agent to something which it has no aptitude for by its own nature. For if something is disposed by its own nature to receive motion from an external agent, such motion will not be forced but natural. This is evident in the motion of the celestial bodies by separate substances, and in that of lower bodies by higher ones.
836. And from this (420).
Here he reduces all of the senses in which things are necessary to one; and in regard to this he does three things. First (836), he shows that all the types of necessity found in reality pertain to this last type. Second (838), he shows that necessity in matters of demonstration is taken in this last sense (“Further, demonstration”). Third (839), he draws a corollary from what has been set down above (“Now of necessary things”).
He accordingly says, first, that all the other senses of the term necessary are somehow referred to this last sense. He makes this clear, first, with reference to the third way in which things are said to be necessary. For whatever is forced is said to do or to undergo something of necessity on the grounds that it cannot act through its own power because of the force exerted on it by an agent; and this is a kind of necessity by which it cannot be otherwise than it is.
837. Then he shows that the same thing is true of the first and second ways in which things are said to be necessary: in the first way with reference to the causes of living and being absolutely, and in the second with reference to the causes of good. For the term necessary was so used in these other ways: in one way to designate that without which a thing cannot be well off, and in the other to designate that without which a thing cannot live or exist. Hence that cause without which a thing cannot live or exist or possess a good or avoid an evil is said to be necessary; the supposition being that the primary notion of the necessary derives from the fact that something cannot be otherwise.
838. Further, demonstration (421).
Then he shows that the necessary in matters of demonstration is taken from this last sense, and this applied both to principles and to conclusions. For demonstration is said to be about necessary things, and to proceed from necessary things. At is said to be about necessary things because what is demonstrated in the strict sense cannot be otherwise. He says “demonstrated in the strict sense” in order to distinguish this from what is demonstrated by the kind of demonstration which refutes an opponent, and does not strictly demonstrate. In the fourth book (609) he called this an ad hominem argument. In demonstrations of this kind which refute an opponent we conclude to the impossible from certain impossible premises. But since in demonstrations the premises are the causes of the conclusion, for demonstrations in the strict sense are productive of science and this is had only by way of a cause, the principles from which a syllogism proceeds must also be necessary and thus cannot be otherwise than they are. For a necessary effect cannot come from a non-necessary cause.
839. Now of necessary things (422).
Here he draws three conclusions from the points set down above, one of which follows from the other. The first is that, since in demonstrations the premises are the causes of the conclusion and both of these are necessary, it follows that some things are necessary in one of two ways. For there are (1) some things whose necessity is caused by something else, and there are (2) others whose necessity has no cause; and such things are necessary of themselves. This is said against Democritus, who claimed that we must not look for the causes of necessary things, as is stated in Book VIII of the Physics.
840. The second conclusion is that, since there must be one first necessary being from which other beings derive their necessity (for there cannot be an infinite regress in causes, as was shown in the second book (301), this first necessary being, which is also necessary in the most proper sense because it is necessary in all ways, must be simple. For composite things are changeable and thus can be in more ways than one. But things which can be in more ways than one can be now in one way and now in another, and this is opposed to the notion of necessity; for that is necessary which cannot be otherwise. Hence the first necessary being must not be now in one way and now in another, and consequently cannot be in more ways than one. Thus he must be simple.
841. The third conclusion is that, since the forced is something which is moved by an external agent in opposition to its own nature, and necessary principles are simple and unchangeable, as has been shown (422:C 840), therefore if there are certain eternal and unchangeable beings, as the separate substances are, in them there must be nothing forced or contrary to their nature. He says this lest a mistake should be made in the case of the term necessity, since it is predicated of immaterial substances without implying on this account that anything forced is found in them.

LESSON 7
The Kinds of Accidental Unity and of Essential Unity
ARISTOTLE'S TEXT Chapter 6: 1015b 16-1016b 3
423. The term one is used both of what is accidentally one and of what is essentially one. A thing is said to be accidentally one, for example, when we say "Coriscus" and "musical" and "musical Coriscus." For to say "Coriscus" and "musical" and "musical Coriscus" amounts to the same thing; and this is also true when we say "just" and "musical" and "just musical Coriscus." For all of these are said to be accidentally one; just and musical because they are accidents of one substance, and musical and Coriscus because the one is an accident of the other. And similarly in a sense musical Coriscus is one with Coriscus, because one of the parts of this expression is an accident of the other. Thus musical is an accident of Coriscus and musical Coriscus is an accident of just Coriscus, because one part of each expression is an accident of one and the same subject. For it makes no difference whether musical is an accident of Coriscus [or whether just Coriscus is an accident of musical Coriscus]. The same thing also holds true if an accident is predicated of a genus or of any universal term, for example, when one says that man and musical man are the same; for this occurs either because musical is an accident of man, which is one substance, or because both are accidents of some singular thing, for example, Coriscus. Yet both do not belong to it in the same way, but one perhaps as the genus and substance, and the other as a habit or modification of the substance. Therefore whatever things are said to be accidentally one are said to be such in this way.
424. But in the case of things which are said to be essentially one, some are said to be such by nature of their continuity; for example, a bundle becomes one by means of a binding, and pieces of wood become one by means of glue. And a continuous line, even if it is bent, is said to be one, just as each part [of the human body] is, for example, a leg or an arm. And of these things themselves those which are continuous by nature are one to a greater degree than those which are continuous by art. And that is said to be continuous whose motion is essentially one and cannot be otherwise. And motion is one when it is indivisible, i.e., indivisible in time.
425. Again, all those things are essentially continuous which are one not merely by contact; for if you place pieces of wood so that they touch each other, you will not say that they are one, either one board or one body or any other continuous thing. Hence those things which are continuous throughout are said to be one even though they are bent. And those which are not bent are one to an even greater degree; for example, the lower leg or the thigh is one to a greater degree than the leg, because the motion of the leg may not be one. And a straight line is one to a greater degree than a bent line. But what is bent and angular we refer to as either one or not one, because its motion may be either simultaneous or not. But the motion of a straight line is always simultaneous, and no part of it which has extension is at rest when another moves, as in a bent line.
426. Again, a thing is said to be one in another sense because its underlying subject is uniform in species; and it is uniform in species as those things whose form is indivisible from the viewpoint of sensory perception. And the underlying subject is either one that is primary or one that is last in relation to the end. For wine is said to be one and water is said to be one inasmuch as they are indivisible in species. And all liquids are said to be one, as oil, wine and fluids, because the ultimate subject of all is the same; for all of these are made up of water or of air.
427. And those things are said to be one whose genus is one and differs by opposite differences. And all these things are said to be one because the genus, which is the subject of the differences, is one; for example, man, dog and horse are one because all are animals; and it is such in a way closest to that in which matter is one. And sometimes these things are said to be one in this way, and sometimes in their higher genus, which is said to be the same if those which are higher than these are the last species of the genus; for example, the isosceles and the equilateral triangle are one and the same figure because both are triangles; but they are not the same triangles.
428. Further, any two things are said to be one when the definition expressing the essence of one is indistinguishable from that signifying the essence of the other. For in itself every definition is divisible. And what has increased and what has decreased are one in this way, because their definition is one. An example of this is found in plane figures, which are one in species.
429. And those things are altogether one and in the highest degree whose concept, which grasps their essence, is indivisible and cannot be separated either in time or in place or in its intelligible structure; and of these, all those which are substances are especially such.
COMMENTARY
842. Having given the various senses of the terms which signify causes, the Philosopher now proceeds to do the same thing with those terms which signify in some way the subject of this science. This is divided into two parts. In the first (423:C 843) he gives or distinguishes the different senses of the terms which signify the subject of this science; and in the second (445:C 908) he distinguishes the different senses of the terms which signify the parts of this subject ("Things are said to be the same").
Now the subject of this science can be taken either as that which has to be considered generally in the whole science, and as such it is unity and being, or as that with which this science is chiefly concerned, and this is substance. Therefore, first (423), he gives the different senses of the term one; second (435:C 885) of the term being ("The term being"); and third (440:C 898), of the term substance ("The term substance").
In regard to the first part of this division he does two things. First, he makes a distinction between what is essentially one and what is accidentally one, and he also indicates the various senses in which things are said to be accidentally one. Second (42VC 848), he notes the various senses in which things are said to be essentially one ("But in the case").
843. He says (423), then, that the term one signifies both what is essentially one and what is accidentally one. And he tells us that what is accidentally one we should consider first in the case of singular terms. Now singular terms can be accidentally one in two ways: in one way according as an accident is related to a subject; and in another way according as one accident is related to another. And in both cases three things have to be considered—one composite thing and two simple ones. For if what is accidentally one is considered to be such according as an accident is related to a subject, then there are, for example, these three things: first, Coriscus; second, musical; and third, musical Coriscus. And these three are accidentally one; for Coriscus and what is musical are the same in subject. Similarly when an accident is related to an accident, three terms must be considered: first, musical; second, just; and third, just musical Coriscus. And all these atle said to be accidentally one, but for different reasons.
844. For just and musical, which are two simple terms in the second way, are said to be accidentally one because both are accidents of one and the same subject. But musical and Coriscus, which are two simple terms in the first way, are said to be accidentally one because "the one," namely, musical, "is an accident of the other," namely, of Coriscus. And similarly in regard to the relationship of musical Coriscus to Coriscus (which is the relationship of a composite term to one of two simple terms), these are said to be accidentally one in the first way, because in this expression, i.e., in the complex term, musical Coriscus, one of the parts, namely, musical, is an accident of the other, which is designated as a substance, namely, Coriscus. And for the same reason it can be said that musical Coriscus is one with just Coriscus, which are two composites in the second way, because two of the parts of each composite are accidents of one subject, Coriscus. For if musical and musical Coriscus, and just and just Coriscus, are the same, then whatever is an accident of musical is also an accident of musical Coriscus; and whatever is an accident of Coriscus is also an accident of just Coriscus. Hence, if musical is an accident of Coriscus, it follows that musical Coriscus is an accident of just Coriscus. Therefore it makes no difference whether we say that musical Coriscus is an accident of just Coriscus, or that musical is an accident of Coriscus.
845. But because accidental predicates of this kind are first applied to singular things and then to universals (although the reverse is true of essential predicates), he therefore makes clear that what he showed in the case of singular terms also applies in that of universal terms. He says that, if an accident is used along with the name of a genus or of any universal term, accidental unity is taken in the same way as it is in the above cases when an accident is joined to a singular term; for example, when it is said that man and musical man are accidentally one, although they differ in some respect.
846. For singular substances are neither present in a subject nor predicated of a subject, so that while they are the subject of other things, they themselves do not have a subject. Now universal substances are predicated of a subject but are not present in a subject, so that while they are not the subjects of accidents, they have something as their subject. Hence, when an accident is joined to a singular substance, the expression stating this can only mean that an accident belongs to a singular substance, as musical belongs to Coriscus when Coriscus is said to be musical.
847. But when we say musical man, the expression can mean one of two things: either that musical is an accident of man, by which substance is designated, and from this it derives its ability to be the subject of an accident; or it means that both of these, man and musical, belong to some singular thing, for example, Coriscus, in the way that musical was predicated of just, because these two belong to the same singular thing and in the same way, i.e., accidentally. But perhaps the one term does not belong to the other in the same way, but in the way that universal substance belongs to the singular as a genus, as the term animal, or if it is not a genus, it at least belongs to the substance of the subject, i.e., as an essential predicate, as the term man. But the other term, namely, musical, does not have the character of a genus or essential predicate, but that of a habit or modification of the subject, or whatever sort of accident it may be. He gives these two, habit and modification, because there are some accidents which remain in their subject, such as habits, which are moved with difficulty, and others which are not permanent but transient, such as modifications. It is clear, then, that these are the ways in which things are said to be accidentally one.
Kinds of unity
848. But in the case (424).
Then he gives the ways in which things are essentially one, and in regard to this he does two things. First, he indicates the different senses in which the term one is used; and second (880), the different senses in which the term many is used (“Moreover, it is evident”).
In regard to the first he does two things. First, he gives the different senses in which things are one from the viewpoint of nature, i.e., according to the conditions found in reality; and second (876), from the viewpoint of logic, i.e., according to the considerations of logic (“Further, some things”).
In regard to the first he does two things. First, he distinguishes the different senses in which things are said to be one. Second (872), he indicates a property which accompanies unity (“But the essence of oneness”).
In regard to the first he does two things. First, he sets down the different senses in which things are said to be one. Second (866), he reduces all of them to a single sense (“For in general”).
In the first part he gives five senses in which the term one is used.
849. (1) The first is this: some of the things which are said to be essentially one are such “by nature of their continuity,” i.e., by being continuous, or “because they are continuous,” as another translation says. But things are said to be continuous in two ways; for, as another text says, some things are continuous by reason of something other than themselves, and some in themselves.
850. First, he proceeds to deal with those things which are continuous (a) by reason of something other than themselves. He says that there are things which are continuous as a result of something else; for example, a bundle of sticks is continuous by means of a cord or binding; and in this way too pieces of wood which have been glued together are said to be one by means of the glue. Now there are also two ways in which this occurs, because the continuity of things which are fastened together (i) sometimes takes the form of a straight line, and (ii) sometimes that of a line which is not straight. This is the case, for example, with a bent line having an angle, which results from the contact of two lines in one surface in such a way that they are not joined in a straight line. And it is in this way that the parts of an animal are said to be one and continuous; for example, the leg, which is bent, and contains an angle at the knee, is said to be one and continuous; and it is the same with the arm.
851. But since this kind of continuity which comes about by reason of something else can exist or come to be both by nature and by art, (b) those things which are continuous by nature are one to a greater degree than those which are continuous by art; for the unity that accounts for the continuity of things which are continuous by nature is not extrinsic to the nature of the thing which is made continuous by it, as happens in the case of things which are one by art, in which the binding or glue or something of the sort is entirely extrinsic to the nature of, the things which are joined together. Hence those things which are joined by nature hold the first place among those which are essentially continuous, which are one in the highest degree.
852. In order to make this clear he defines the continuous. He says that that is said to be continuous which has only one motion essentially and cannot be otherwise. For the different parts of any continuous thing cannot be moved by different motions, but the whole continuous thing is moved by one motion. He says “essentially” because a continuous thing can be moved in one way essentially and in another or others accidentally. For example, if a man in a ship moves against the motion of the ship essentially, he is still moved accidentally by the motion of the ship.
853. Now in order for motion to be one it must be indivisible; and by this I mean from the viewpoint of time, in the sense that at the same time that one part of a continuous thing is moved another is also moved. For it is impossible that one part of a continuous thing should be in motion and another at rest, or that one part should be at rest and another in motion, so that the motion of the different parts should take place in different parts of time.
854. Therefore the Philosopher defines the continuous here by means of motion, and not by means of the oneness of the boundary at which the parts of the continuous things are joined, as is stated in the Categories, and in the Physics; because from this definition he can consider different grades of unity in different continuous things (as will be made clear later on [856]), but he cannot do this from the definition given there.
855. Moreover, it should be noted that what is said here about the motion of a continuous thing being indivisible from the viewpoint of time is not opposed to the point proved in Book VI of the Physics, that the time of a motion is divided according to the parts of the thing moved. For here the Philosopher is speaking of motion in an unqualified sense, because one part of a continuous thing does not begin to be moved before another part does; but there he is speaking of some designation which is made in the continuous quantity over which motion passes. For that designation, which is the first part of a continuous quantity, is traversed in a prior time, although in that prior time other parts of the continuous thing that is in motion are also moved.
856. Again, all those (425).
Then he proceeds to deal with things which are essentially continuous. He says that those things are essentially continuous which are said to be one not by contact. He proves this as follows: things which touch each other, as two pieces of wood, are not said to be one piece of wood or one body or any other kind of one which belongs to the class of the continuous. Hence it is evident that the oneness of things which are continuous differs from that of things which touch each other. For those things which touch each other do not have any unity of continuity of themselves but by reason of some bond which unites them; but those things which are continuous are said to be essentially one even though they are bent. For two bent lines are continuous in relation to one common boundary, which is the point at which the angle is formed.
857. Yet those things are one to a greater degree which are essentially continuous and without a bend. The reason is that a straight line can have only one motion in all of its parts, whereas a bent line can have one or two motions. For the whole of a bent line can be understood to be moved in one part; and it can also be understood that when one part is at rest, the other part, which makes an angle with the part at rest, can come closer by its motion to the unmoved part; for example, when the lower leg or shin is bent in the direction of the upper leg, which here is called the thigh. Hence each of these—the shin and thigh—is one to a greater degree “than the scelos,” as the Greek text says, i.e. the whole composed of the shin and thigh.
858. Further, it must be noted that the text which reads “curved” instead of “bent” is false. For, since the parts of a curved line do not contain an angle, it is evident that they must be in motion together or at rest together, just as the parts of a straight line are; but this does not happen in the case of a bent line, as has been stated (857).
859. Again, a thing (426).
(2) Here he gives the second way in which things are one. He says that a thing is said to be one in a second way not merely by reason of continuous quantity but because of the fact that the whole subject is uniform in species. For some things can be continuous even though they differ in species; for example, when gold is continuous with silver or something of this kind. And then two such things will be one if quantity alone is considered but not if the nature of the subject is considered. But if the whole continuous subject is uniform in species, it will be one both from the viewpoint of quantity and from that of nature.
860. Now a subject is said to be uniform in species when the same sensible form is not divided in such a way that there are different sensible forms in different parts of the subject, as it sometimes happens, for example, that one part of a sensible body is white and another black. And this subject, which does not differ in species, can be taken in two ways: in one way as the first subject, and in another as the last or ultimate subject which is reached at the end of a division. It is evident, for example, that a whole amount of wine is said to be one because its parts are parts of one common subject which is undifferentiated specifically. The same is true of water. For all liquids or moist things are said to be one insofar as they have a single ultimate subject. For oil and wine and the like are ultimately dissolved into water or air, which is the root of moistness in all things.
861. And those things (427).
(3) Then he indicates the third way in which things are said to be one. He says that those things are said to be one whose genus is one, even though it is divided by opposite differences. And this way resembles the preceding one; for some things were said to be one in the preceding way because their subject-genus is one, and now some things are said to be one because their genus, which is the subject of differences, is one; for example, a man and a horse and a dog are said to be one because they have animality in common as one genus, which is the subject of differences. Yet this way differs from the preceding, because in the preceding way the subject was one thing which was not differentiated by forms; but here the subject-genus is one thing which is differentiated by various differences, as though by various forms.
862. Thus it is evident that some things are said to be one in genus in a most proximate sense, and in a way similar to that in which some things are said to be one in matter. For those things which are said to be one in matter are also differentiated by forms. For even though a genus is not matter, because it would then not be predicated of a species since matter is part of a thing, still the notion of a genus is taken from what is material in a thing, just as the notion of a difference is taken from what is formal. For the rational soul is not the difference of man (since it is not predicated of man), but something having a rational soul (for this is what the term rational signifies). Similarly, sensory nature is not the genus of man but a part. But something having a sensory nature, which the term animal Signifies, is the genus of man. In a similar fashion, then, the way in which things are one in matter is closely related to that in which they are one in genus.
863. But it must be borne in mind that to he one in generic character has two meanings. For sometimes some things are said to be one in genus, as has been stated, because they belong to one genus, whatever it may be. But sometimes some things are said to be one in genus only in reference to a higher genus, which, along with the designation “one” or “the same,” is predicated of the last species of a lower genus when there are other higher species in one of which the lower species agree. For example, figure is one supreme genus which has many species under it, namely, circle, triangle, square, and the like. And triangle also has different species, namely, the equilateral, which is called iso-pleural and the triangle with two equal sides, which is called equi-legged or isosceles. Hence these two triangles are said to be one figure, which is their remote genus, but not one triangle, which is their proximate genus. The reason for this is that these two triangles do not differ by any differences which divide figure, but by differences which divide triangle. And the term same means that from which something does not differ by a difference.
864. (4) He now describes the fourth way in which things are said to be one. He says that things such that the definition of one (which is the concept signifying its quiddity) is not distinguished from the definition of the other (which also signifies its quiddity) are also said to be one. For while every definition must be divisible or distinguishable in itself, or essentially, since it is composed of genus and difference, it is possible for the definition of one thing to be indistinguishable from that of another when the two have one definition. And this applies (a) whether those definitions signify the total [intelligible structure] of the thing defined, as tunic and clothing (and then things whose definition is one are one in an absolute sense), or (b) whether that common definition does not totally comprehend the intelligible structure of the two things which have it in common, as an ox and a horse have in common the one definition of animal. Hence they are never one in an absolute sense, but only in a relative sense inasmuch as each is an animal. The same applies in the case of increase and decrease; for there is one common definition of the genus, because each is a motion relating to quantity. And the same thing is true of plane figures, for there is one definition of the species, plane figure.
865. And those things (429).
(5) He gives the fifth way in which things are one. He says that those things are “ altogether ” one, i.e., perfectly, and in the highest degree, whose concept, which grasps their quiddity, is altogether indivisible, like simple things, which are not composed of material and formal principles. Hence the concept which embraces their quiddity does not comprehend them in such a way as to form a definition of them from different principles, but (a) rather grasps them negatively, as happens in the case of a point, which has no parts; or (b) it even comprehends them by relating them to composite things, as happens, for example, when someone defines the unit as the principle of number. And because such things have in themselves an indivisible concept, and things which are divided in any way at all can be understood separately, it therefore follows that such things are indivisible both in time and in place and in their intelligible structure. Hence these things are one in the highest degree, and especially those which are indivisible in the genus of substance. For even though what is indivisible in the genus of accident is not composite in itself, nonetheless it does form a composite with something else, namely, the subject in which it inheres. But an indivisible substance is neither composite in itself nor does it form a composite with something else. Or the term substance can be taken in the ablative case, and then the sense is that, even though some things are said to be one because they are indivisible in time and in place and in definition, still those things in this class which are indivisible in substance are said to be one in the highest degree. This sense is reduced to the preceding one.

LESSON 8
The Primary Sense of One. One in the Sense of Complete. One as the Principle of Number. The Ways in Which Things Are One. The Ways in Which Things Are Many
ARISTOTLE'S TEXT Chapter 6: 1016b 3-1017a 6
430. For in general those things which do not admit of division are said to be one insofar as they do not admit of division. Thus, if two things do not admit of division insofar as they are man, they are one man; and if they do not admit of division insofar as they are animal, they are one animal; and if they do not admit of division insofar as they have continuous quantity, they are one continuous quantity. Hence many things are said to be one because they do or undergo or have or are related to 1 some other thing which is one. But those things are said to be one in a primary sense whose substance is one; and they are one either by continuity or in species or in intelligible structure. For we count as many those things which are not continuous, or those whose form is not one, or those whose intelligible structure is not one.
431. Again, in one sense we say that anything at all is one by continuity if it is quantitative and continuous; and in another sense we say that a thing is not one unless it is a whole, i.e., unless it has one form. Thus in looking at the parts of a shoe which are put together in any way at all, we would not say that they are one, except by reason of their continuity; but if they are put together in such a way as to be a shoe and to have a certain form, there would then be one thing. And for this reason, among lines the circular line is one in the highest degree because it is whole and complete.
432. But the essence of oneness is to be a principle of some number; for the first measure is a principle, because that by which we first come to know each class of things is its first measure. Unity, then, is the first principle of what is knowable about each class. But this unity or unit is not the same in all classes; for in one it is the lesser half tone, and in another it is the vowel or consonant; and in the case of weight the unit is different; and in that of motion different still. But in all cases what is one is indivisible either in quantity or in species. Thus a unit is indivisible in quantity as quantity in every way and has no position; and a point is indivisible in every way and has position. A line is divisible in one dimension; a surface, in two; and a body, in three. And conversely, that which is divisible in two dimensions is a surface; in one, a line; and quantitatively indivisible in every way, a point and a unit. If it has no position, it is a unit; and if it has position, it is a point.
433. Further, some things are one in number, some in species, some in genus, and some analogically or proportionally. Those things are one in number which have one matter; in species, which have one intelligible structure; in genus, which have the same figure of predication; and proportionally, which are related to each other as some third thing is to a fourth. And the latter types of unity always follow the former. Thus things which are one in number are one in species, but not all which are one in species are one in number; and all which are one in species are one in genus, but not all which are one in genus are one in species, although they are all one proportionally. And not all which are one proportionally are one in genus.
434. Moreover, it is evident that things are said to be many in a way opposite to that in which they are one. For some things are many because they are not continuous; others, because their matter, either the first or ultimate, is divisible in species; and others because they have many conceptions expressing their essence.
COMMENTARY
How the kinds of unity inter-relate
866. Here the Philosopher reduces all senses in which things are said to be one to one primary sense, and in regard to this he does two things. First, he makes this reduction; and second (870), to those senses in which things are said to be one, which have already been given, he adds another (“Again, in one sense”).
He accordingly says, first, that it is evident from what precedes that things which are indivisible in every way are said to be one in the highest degree. For all the other senses in which things are said to be one are reducible to this sense, because it is universally true that those things which do not admit of division are said to be one insofar as they do not admit of division. For example, those things which are undivided insofar as they are man are said to be one in humanity, as Socrates and Plato; those which are undivided in the notion of animality are said to be one in animality; and those which are undivided from the viewpoint of extension or measure are said to be one in quantity, as continuous things.
867. And from this we can also derive number and the types of unity given above, because what is one is indivisible either in an absolute sense or in a qualified one. (5) If it is indivisible in an absolute sense, it is the last type of unity, which is a principle; but if it is indivisible in a qualified sense, it is so either in quantity alone or in nature. (1) If it is indivisible in quantity, then it is the first type. If it is indivisible in nature, it is so either in reference to its subject or to the division which depends upon the form. If it is divisible in reference to its subject, (2) it is so either in reference to a real subject, and then it is the second type, or (3) to a logical subject, and then it is the third type. (4) And indivisibility of form, which is indivisibility of intelligible structure, or definition, constitutes the fourth type.
868. Now from these senses of the term one certain others are again derived. Thus there are many things which are said to be one because they are doing one thing. For example, many men are said to be one insofar as they are rowing a boat. And some things are said to be one because they are subject to one thing; for example, many men constitute one people because they are ruled by one king. And some are said to be one because they possess one thing; for example, many owners of a field are said to be one in their ownership of it. And some things are also said to be one because they are something which is one; for example, many men are said to be one because each of them is white.
869. But considering all of these secondary senses in which things are said to be one, which have already been stated in the five ways given above, we can say that those things are one in the primary sense which are one in their substance.(1) For a thing is one in substance either by reason of its continuity, as in the first way; or (2) because of the species of the subject, as in the second way; (3) and again in the third way because the unity of the genus is somewhat similar to the unity of the species; or also (4 & 5) because of the intelligible structure, as in the fourth and fifth ways. That some things are said to be one in these ways is clear from the opposite of one. For things are many in number, i.e., they are counted as many, either because they are continuous, or because they do not have one species, or because they do not have one common intelligible structure.
870. Again, in one sense (430
Then he gives an additional sense in which the term one is used, which differs from the preceding ones. This sense is not derived from thr- notion of indivision, as the foregoing are, but rather from the notion of division. He says that sometimes some things are said to be one because of continuity alone, and sometimes they are said to be one only if they constitute a whole and something complete. Now this happens when the thing has one form, not in the sense that a homogeneous subject is said to have one form, which pertains to the second type given above, but in the sense that the form consists in a kind of totality requiring a definite order of parts. Thus it is clear that we do not say that a thing is one, for example, some artifact such as a shoe, when we see the parts put together in any way at all (unless perhaps it is taken to be one insofar as it is continuous); but we say that all parts of a shoe are one when they are united in such a way that the thing is a shoe and has one form-that of a shoe.
871. And from this it is clear that a circular line is one in the highest degree. For a circular line is not only continuous like a straight line, but also has a totality and completeness which a straight line does not have; for that is complete and whole which lacks nothing. Now this characteristic belongs to a circular line; for nothing can be added to a circular line, but something can be added to a straight one.
872. But the essence (432).
Then he indicates a property which flows from oneness or unity. He says that the essence of one consists in being the principle of some number. This is clear from the fact that the unit is the primary numerical measure by which every number is measured. Now a measure has the character of a principle, because measured things are known by their measure, and things are known by their proper principles. And it is clear from this that unity is the first principle of what is known or knowable about each thing, and that it is the principle of knowing in all classes.
873. But this unity which is the principle of knowing is not the same in all classes of things. For in the class of musical sounds it is the lesser half tone, which is the smallest thing in this class; for a lesser half tone is less than a half tone since a tone is divided into two unequal half tones one of which is called a lesser half tone. And in the class of words the first and smallest unity is the vowel or consonant; and the vowel to a greater degree than the consonant, as will be stated in Book X (831:C 1971). And in the class of heavy things or weights there is some smallest thing which is their measure, i.e., the ounce or something of this kind. And in the class of motions there is one first measure which measures the other motions, namely, the simplest and swiftest motion, which is the diurnal motion.
874. Yet all of these have this feature in common that the first measure is indivisible in quantity or in species. Hence, in order that something be one and first in the genus of quantity it must be indivisible, and indivisible in quantity. It is called a unit if it is indivisible in every way and has no position, and a point if it is altogether indivisible in quantity but has position. A line is something divisible in one dimension only; a surface, in two; and a body, in all, i.e., in three dimensions. And these descriptions are reversible; for everything that is divisible in two dimensions is a surface, and so on with the others.
875. Again, it must be noted that being a measure is the distinctive characteristic of unity insofar as it is the principle of number. But this unity or one is not the same as that which is interchangeable with being, as has been stated in Book IV (303:C 557). For the concept of the latter kind of unity involves only being undivided, but that of the former kind involves being a measure. But even though this character of a measure belongs to the unity which is the principle of number, still by a kind of likeness it is transferred to the unity found in other classes of things, as the Philosopher will show in Book X of this work (814:C 1921). And according to this the character of a measure is found in any class of things. But this character of a measure is a natural consequence of the note of undividedness, as has been explained (432:C 872). Hence the term one is not predicated in a totally equivocal sense of the unity which is interchangeable with being and of that which is the principle of number, but it is predicated of one primarily and of the other secondarily.
876. Further, some things (433).
Then he gives another way of dividing unity, and this division is rather from the viewpoint of logic. He says that some things are one in number, some in species, some in genus, and some analogically.
Those things are one in number whose matter is one; for insofar as matter has certain designated dimensions it is the principle by which a form is individuated. And for this reason a singular thing is numerically one and divided from other things as a result of matter.
877. Those things are said to be one in species which have one “intelligible structure,” or definition; for the only thing that is defined in a proper sense is the species, since every definition is composed of a genus and a difference. And if any genus is defined, this happens in so far as it is a species.
878. Those things are one in genus which have in common one of the “figures of predication,” i.e., which have one way of being predicated. For the way in which substance is predicated and that in which quality or action is predicated are different; but all substances have one way of being predicated inasmuch as they are not predicated as something which is present in a subject.
879. And those things are proportionally or analogically one which agree in this respect that one is related to another as some third thing is to a fourth. Now this can be taken in two ways: (1) either in the sense that any two things are related in different ways to one third thing (for example, the term healthy is predicated of urine because it signifies the relationship of a sign of health [to health itself]; and of medicine because it signifies the relationship of a cause to the same health); (2) or it may be taken in the sense that the proportion of two things to two other things is the same (for example, tranquillity to the sea and serenity to the air; for tranquillity is a state of rest in the sea, and serenity is a state of rest in the air).
880. Now with regard to the ways in which things are one, the latter types of unity always follow the former, and not the reverse; for those things which are one in number are one in species, but not the other way about. The same thing is clear in the other cases.
881. Moreover, itis evident (434).
From the ways in which things are said to be one he now derives the ways in which things are said to be many. He says that things are said to be many in just as many ways as they are said to be one, because in the case of opposite terms one is used in as many ways as the other.
(1) Hence some things are said to be many because they are not continuous, which is the opposite of the first way in which things are one.
882. (2 & 3) Other things are said to be many because their matter is divisible in species, whether we understand by matter “the first,” i.e., their proximate matter, or the final or ultimate matter into which they are ultimately dissolved. Indeed, it is by the division of their proximate matter that wine and oil are said to be many, and by the division of their remote matter that wine and a stone are said to be many. And if matter be taken both for real matter and for conceptual matter, i.e., for a genus, which resembles matter, many in this sense is taken as the opposite of the second and third ways in which things are said to be one.
883. (4) And still other things are said to be many when the conceptions which express their essence are many. And many in this sense is taken as the opposite of the fourth way in which things are said to be one.
884. (5) But the opposite of the fifth way in which things are one does not have the notion of many except in a qualified sense and potentially; for the fact that a thing is divisible does not make it many except potentially.

LESSON 9
Division of Being into Accidental and Essential. The Types of Accidental and of Essential Being
ARISTOTLE'S TEXT Chapter 7: 1017a 7-1017b 9
435. The term being (ens) signifies both accidental being (ens per accidens) and essential being (ens per se).
436. Accidental being is designated when we say, for example, that the just person is musical, and that the man is musical, and that the musician is a man. And the same thing applies when we say that the musician builds, because it is accidental to a builder to be a musician, or to a musician to be a builder. For to say that "this is that" means that this is an accident of that. And so it is in the cases given; for when we say that the man is musical, and that the musician is a man, or that what is musical is white, in the latter case we mean that both are accidents of the same thing, and in the former that the attribute is accidental to the being. But when we say that what is musical is a man, we mean that musical is an accident of this person. And in this sense too white is said to be, because the thing of which it is an accident is. Therefore those things which are said to be in an accidental sense are said to be such either because both belong to the same being, or because the attribute belongs to the being, or because the thing to which it belongs and of which it is predicated is.
437. On the other hand those things are said to be essentially which signify the figures of predication; 1 for being is signified in just as many ways as predications are made. Therefore, since some of these predications signify what a thing is, others what it is like, others how much, others how related, others what it does, others what it undergoes, others where, and others when, to each of these there corresponds a mode of being which signifies the same thing. For there is no difference between "the man is recovering" and "the man recovers," or between "the man is walking" or "cutting" and "the man walks" or "cuts." And the same is true in other cases.
438. Again, being signifies that something is true, and non-being signifies that something is not true but false. This also holds true of affirmation and negation. For example, to say that Socrates is musical means that this is true. Or to say that Socrates is not white means that this is true. But to say that the diagonal of a square is not incommensurable with a side means that this is false.
439. Again, to be, or being, signifies that some of the things mentioned are potentially and others actually. For in the case of the terms mentioned we predicate being both of what is said to be potentially and of what is said to be actually. And similarly we say both of one who is capable of using scientific knowledge and of one who is actually using it, that he knows. And we say that that is at rest which is already so or capable of being so. And this also applies in the case of substances; for we say that Mercury is in the stone, and half of the line in the line, and we call that grain which is not yet ripe. But when a thing is potential and when not must be settled elsewhere (773: C 1832).
COMMENTARY
Kinds of being: Three ways per accidens
885. Here the Philosopher gives the various senses in which the term being is used, and in regard to this he does three things. First, he divides being into essential being and accidental being. Second (886), he distinguishes between the types of accidental being (“Accidental being”). Third (889), he distinguishes between the types of essential being (“On the other hand”).
He says, then, that while things are said to be both essentially and accidentally, it should be noted that this division of being is not the same as that whereby being is divided into substance and accident. This is clear from the fact that he later divides essential being into the ten predicaments, nine of which belong to the class of accident (889). Hence being is divided into substance and accident insofar as it is considered in an absolute sense; for example, whiteness considered in itself is called an accident, and man a substance. But accidental being, in the sense in which it is taken here must be understood by comparing an accident with a substance; and this comparison is signified by the term is when, for example, it is said that the man is white. Hence this whole “the man is white” is an accidental being. It is clear, then, that the division of being into essential being and accidental being is based on the fact that one thing is predicated of another either essentially or accidentally. But the division of being into substance and accident is based on the fact that a thing is in its own nature either a substance or an accident.
886. Then he indicates the various senses in which a thing is said to be accidentally. He says that this occurs in three ways: (1) first, when an accident is predicated of an accident, as when it is said that someone just is musical: (2) second, when an accident is predicated of a subject, as when it is said that the man is musical; and (3) third, when a subject is predicated of an accident, as when it is said that the musician is a man. And since he has shown above (787) how an accidental cause differs from an essential cause, he therefore now shows that an accidental being is a result of an accidental cause.
887. He says that in giving an accidental cause we say that the musician builds, because it is accidental to a builder to be a musician, or vice versa; for it is evident that the statement “this is that,” i.e., the musician is a builder, simply means that “this is an accident of that.” The same is true of the foregoing senses of accidental being when we say that the man is musical by predicating an accident of a subject, or when we say that what is white is musical, or conversely that what is musical is white by predicating an accident of an accident. For in all of these cases is signifies merely accidental being: “in the latter case,” i.e., when an accident is predicated of an accident, is signifies that both accidents are accidental to the same subject; “and in the former,” i.e., when an accident is predicated of a subject, is signifies “that the attribute is accidental to the being,” i.e., to the subject. But when we say that what is musical is a man, we mean “that musical is an accident of this person,” i.e., that musical, which holds the position of a subject, is an accident of the predicate. And the reason for making the predication is similar in a sense when a subject is predicated of an accident and when an accident is predicated of an accident. For a subject is predicated of an accident by reason of the fact that the subject is predicated of that to which the accident, which is expressed in the subject, is accidental; and in a similar fashion an accident is predicated of an accident because it is predicated of the subject of an accident. And for this reason the attribute musical is predicated not only of man but also of white, because that of which the attribute musical is an accident, i.e., the subject, is white.
888. It, is evident, then, that those things which are said to be in an accidental sense are said to be such for three reasons: (1) either “because both,” namely, the subject and predicate, belong to the same thing (as when an accident is predicated of an accident); or (2) “because the attribute,” namely, the predicate, such as musical, “belongs to the being,” i.e., to the subject which is said to be musical (and this occurs when an accident is predicated of a subject); or (3) “because the thing,” i.e., the subject which is expressed in the predicate, to which belongs the accident of which it (the subject) is itself predicated, itself is (and this occurs when a subject is predicated of an accident, as when we say that what is musical is a man).
Ten ways per se
889. On the other hand (437).
Here he distinguishes between the types of essential being; and in regard to this he does three things. First, he divides the kind of being which lies outside the mind, which is complete being, by the ten predicaments. Second (895), he gives another type of being, inasmuch as being exists only in the mind (“Again, being, signifies”). Third (897), he divides being by potentiality and actuality— and being divided in this way is more common than complete being, for potential being is being only imperfectly and in a qualified sense (“Again, to be”).
He says, first (437), that all those things which signify the figures of predication are said to be essentially. For it must be noted that being cannot be narrowed down to some definite thing in the way in which a genus is narrowed down to a species by means of (-) differences. For since a difference does not participate in a genus, it lies outside the essence of a genus. But there could be nothing outside the essence of being which could constitute a particular species of being by adding to being; for what is outside of being is nothing, and this cannot be a difference. Hence in Book III of this work (433) the Philosopher proved that being cannot be a genus.
890. Being must then be narrowed down to diverse genera on the basis of a (+) different mode of predication, which flows from a different mode of being; for “being is signified,” i.e., something is signified to be, “in just as many ways” (or in as many senses) as we can make predications. And for this reason the classes into which being is first divided are called predicaments, because they are distinguished on the basis of different ways of predicating. Therefore, since some predicates signify what (i.e., substance); some, of what kind; some, how much; and so on; there must be a mode of being corresponding to each type of predication. For example, when it is said that a man is an animal, is signifies substance; and when it is said that a man is white, is signifies quality; and so on.
891. For it should be noted that a predicate can be referred to a subject in three ways.
(1) This occurs in one way when the predicate states what the subject is, as when I say that Socrates is an animal; for Socrates is the thing which is an animal. And this predicate is said to signify first substance, i.e., a particular substance, of which all attributes are predicated.
892. (2) A predicate is referred to a subject in a second way when the predicate is taken as being in the subject, and this predicate is in the subject either (a) essentially and absolutely and (i) as something flowing from its matter, and then it is quantity; or (ii) as something flowing from its form, and then it is quality; or (b) it is not present in the subject absolutely but with reference to something else, and then it is relation.
(3) A predicate is referred to a subject in a third, way when the predicate is taken from something extrinsic to the subject, and this occurs in two ways. (a) In one way, that from which the predicate is taken is totally extrinsic to the subject; and (i) if this is not a measure of the subject, it is predicated after the manner of attire, as when it is said that Socrates is shod or clothed. (ii) But if it is a measure of the subject, then, since an extrinsic measure is either time or place, (aa) the predicament is taken either in reference to time, and so it will be when; or (bb) if it is taken in reference to place and the order of parts in place is not considered, it will be where; but if this order is considered, it will be position. (b) In another way, that from which the predicate is taken, though outside the subject, is nevertheless from a certain point of view in the subject of which it is predicated. (i) And if it is from the viewpoint of the principle, then it is predicated as an action; for the principle of action is in the subject. (ii) But if it is from the viewpoint of its terminus, then it will be predicated as a passion; for a passion is terminated in the subject which is being acted upon.
893. But since there are some predications in which the verb is is clearly not used (for example, when it is said that a man walks), lest someone think that these predications do not involve the predication of being, for this reason Aristotle subsequently rejects this, saying that in all predications of this kind something is signified to be. For every verb is reduced to the verb is plus a participle. For there is no difference between the statements “the man is recovering” and “the man recovers”; and it is the same in other cases. It is clear, then, that “being” is used in as many ways as we make predications.
894. And there is no truth in Avicenna’s statement that predicates which belong to the class of accidents primarily signify substance and secondarily accidents, as the terms white and musical. For the term white, as it is used in the categories, signifies quality alone. Now the term white implies a subject inasmuch as it signifies whiteness after the manner of an accident, so that it must by implication include the subject in its notion, because the being of an accident consists in being in something. For even though whiteness signifies an accident, it still does not signify this after the manner of an accident but after that of a substance. Hence it implies a subject in no way. For if it were to signify a subject primarily, then the Philosopher would not put accidental predicates under essential being but under accidental being. For the whole statement “the man is white” is a being in an accidental sense, as has been stated (886).
Logical being
895. Again, being signifies (438).
Then he gives another sense in which the term being is used, inasmuch as the terms being and is signify the composition of a proposition, which the intellect makes when it combines and separates. He says that being signifies the truth of a thing, or as another translation better expresses it, being signifies that some statement is true. Thus the truth of a thing can be said to determine the truth of a proposition after the manner of a cause; for by reason of the fact that a thing is or is not, a discourse is true or false. For when we say that something is, we signify that a proposition is true; and when we say that something is not, we signify that it is not true. And this applies both to affirmation and to negation. It applies to affirmation, as when we say that Socrates is white because this is true; and to negation, as when we say that Socrates is not white, because this is true, namely, that he is not white. And in a similar way we say that the diagonal of a square is not incommensurable with a side, because this is false, i.e., its not being incommensurable.
896. Now it must be noted that this second way in which being is used is related to the first as an effect is to a cause. For from the fact that something is in reality it follows that there is truth and falsity in a proposition, and the intellect signifies this by the term is taken as a verb copula. But since the intellect considers as a kind of being something which is in itself a non-being, such as a negation and the like, therefore sometimes being is predicated of something in this second way and not in the first. For blindness is said to be in the second way on the grounds that the proposition in which something is said to be blind is true. However, it is not said to be true in the first way; for blindness does not have any being in reality but is rather a privation of some being. Now it is accidental to a thing that an attribute should be affirmed of it truly in thought or in word, for reality is not referred to knowledge but the reverse. But the act of being which each thing has in its own nature is substantial; and therefore when it is said that Socrates is, if the is is taken in the first way, it belongs to the class of substantial predicates; for being is a higher predicate with reference to any particular being, as animal with reference to man. But if it is taken in the second way, it belongs to the class of accidental predicates.
Division by potency and act
897. Again, to be, or being (439).
Here he gives the division of being into the actual and the potential. He says that to be and being signify something which is expressible or utterable potentially or actually. For in the case of all of the foregoing terms which signify the ten predicaments, something is said to be so actually and something else potentially; and from this it follows that each predicament is divided by actuality and potentiality. And just as in the case of things which are outside the mind some are said to be actually and some potentially, so also is this true in the case of the mind’s activities, and in that of privations, which are only conceptual beings. For one is said to know both because he is capable of using scientific knowledge and because he is using it; and similarly a thing is said to be at rest both because rest belongs to it already and because it is capable of being at rest. And this is true not only of accidents but also of substances. For “Mercury,” we say, i.e., the image of Mercury, is present potentially in the stone; and half of a line is present potentially in a line, for every part of a continuum is potentially in the whole. And the line is included in the class of substances according to the opinion of those who hold that the objects of mathematics are substances—an opinion which he has not yet disproved. And when grain is not yet ripe, for example, when it is still in blade, it is said to be potentially. Just when, however, something is potential and when it is no longer such must be established elsewhere, namely, in Book IX of this work (1832).

LESSON 10
Meanings of Substance
ARISTOTLE'S TEXT Chapter 8: 1017b 10-1017b 26
440. The term substance (substantia) means the simple bodies, such as earth, fire, water and the like; and in general bodies and the things composed of them, both animals and demons and their parts. All of these are called substances because they are not predicated of a subject, but other things are predicated of them.
441. In another sense substance means that which, being present in such things as are not predicated of a subject, is the cause of their being, as the soul in an animal.
442. Again, substance means those parts which, being present in such things, limit them and designate them as individuals and as a result of whose destruction the whole is destroyed; for example, body is destroyed when surface is, as some say, and surface when line is. And in general it seems to some that number is of this nature; for [according to them] if it is destroyed, nothing will exist, and it limits all things.
443. Again, the quiddity of a thing, whose intelligible expression is the definition, also seems to be the substance of each thing.
444. It follows, then, that the term substance is used in two senses. It means the ultimate subject, which is not further predicated of something else; and it means anything which is a particular being and capable of existing apart. The form and species of each thing is said to be of this nature.
COMMENTARY
Lesson 10
Kinds of substance
898. Aristotle now explains the various senses in which the term substance is used; and in regard to this he does two things. First, he gives the various senses in which the term substance is used. Second (903), he reduces all of these to two (“It follows”).
In treating the first part he gives four senses of the term substance.
(1) First, it means particular substances, such as the simple bodies: earth, fire, water and the like. And in general it means all bodies, even though they are not simple, i.e., compound bodies of like parts, such as stones, blood, flesh and the like. Again, it means animals, which are composed of such sensible bodies, and also their parts, such as hands and feet and so on; “and demons,” i.e., the idols set up in temples and worshipped as gods. Or by demons he means certain animals which the Platonists claimed are capable of reasoning, and which Apuleius defines thus: demons are animals composed of an ethereal body, rational in mind, passive in soul, and eternal in time. Now all of the foregoing things are called substances because they are not predicated of another subject but other things are predicated of them. This is the description of first substance given in the Categories.
899. In another sense (411).
(2) He says that in another sense substance means the cause of the being of the foregoing substances which are not predicated of a subject; and it is not extrinsic to them like an efficient cause but is intrinsic like a form. It is in this sense that the soul is called the substance of an animal.
900. Again, substance (442).
(3) He gives a third meaning of substance, which is the one used by the Platonists and Pythagoreans. He says that all those parts of the foregoing substances which constitute their limits and designate them as individuals, according to the opinion of these thinkers, and by whose destruction the whole is destroyed, are also termed substances. For example, body is destroyed when surface is, as some say, and surface when line is. It is also clear that surface is the limit of body and line the limit of surface. And according to the opinion of the philosophers just mentioned the line is a part of surface and surface a part of body. For they held that bodies are composed of surfaces, surfaces of lines, and lines of points; and thus it would follow that the point is the substance of the line, the line the substance of surface, and so on for the rest. And according to this position number seems to constitute the entire substance of all things, because when number is destroyed nothing remains in the world; for what is not one is nothing. And similarly things which are not many are non-existent. And number is also found to limit all things, because all things are measured by number.
901. But this sense of substance is not a true one. For that which is found to be common to all things and is something without which they cannot exist does not necessarily constitute their substance, but it can be some property flowing from the substance or from a principle of the substance. These philosophers also fell into error especially regarding unity and number because they failed to distinguish between the unity which is interchangeable with being and that which is the principle of number.
902. Again, the quiddity (443).
(4) He says that the quiddity of each thing, which the definition signifies, is also called its substance. Now the quiddity or essence of a thing, whose intelligible expression is the definition, differs from a form, which he identified with the second meaning of substance, just as humanity differs from a soul, for a form is part of a thing’s essence or quiddity, but the essence or quiddity itself of a thing includes all its essential principles. It is in this last sense, then, that genus and species are said to be the substance of the things of which they are predicated; for genus and species do not signify the form alone but the whole essence of a thing.
903. It follows (444).
Then he reduces the foregoing senses of substance to two. He says that from the above-mentioned ways in which the term substance is used we can understand that it has two meanings. (1) It means the ultimate subject in propositions, and thus is not predicated of something else. This is first substance, which means a particular thing which exists of itself and is capable of existing apart because it is distinct from everything else and cannot be common to many. (2) And a particular substance differs from universal substance in these three respects: first, a particular substance is not predicated of inferiors, whereas a universal substance is; second, universal substance subsists only by reason of a particular substance, which subsists of itself; and third, universal substance is present in many things, whereas a particular substance is not but is distinct from everything else and capable of existing apart.
904. And the form and species of a thing also “is said to be of this nature,” i.e., substance. In this he includes the second and fourth senses of substance; for essence and form have this note in common that both are said to be that by which something is. However, form, which causes a thing to be actual, is related to matter, whereas quiddity or essence is related to the supposit, which is signified as having such and such an essence. Hence “the form and species” are comprehended under one thing—a being’s essence.
905. He omits the third sense of substance because it is a false one, or because it is reducible to form, which has the character of a limit. And he omits matter, which is called substance, because it is not substance actually. However, it is included in the first sense of substance, because a particular substance is a substance and is individuated in the world of material things only by means of matter.

LESSON 11
The Ways in Which Things Are the Same Essentially and Accidentally
ARISTOTLE'S TEXT Chapter 9: 1017b 27-1018a 9
445. Things are said to be the same accidentally; for example, "white" and musical" are the same because they are accidents of the same subject. And "man" and "musical" are the same because the one is an accident of the other. And,'musical" is the same as "man" because it is an accident of a man. And the composite is the same as each of these simple terms, and each the same as it. For both "man" and "musical" are said to be the same as "musical man," and this the same as they. And for this reason none of these predications are universal. For it is not true to say that every man is the same as the musical; for universal predicates are essential, whereas accidental predicates are not ' but are said of singulars in an unqualified sense. For "Socrates" and "musical Socrates" seem to be the same because Socrates is not found in many. And for this reason we do not say "every Socrates" as we say "every man." Some things, then, are said to be the same in this way.
446. And others are said to be the same essentially, and in the same number of ways in which they are said to be one. For those things whose matter is one in species or in number, and those whose substance is one, are said to be the same. Hence it is evident that sameness (identitas) is a kind of unity of the being of many things or of one thing taken as many; for example, when a person says that something is the same as itself, he uses the same thing as though it were two.
COMMENTARY
906. Having given the various senses of the terms which signify the subject of this science, here the Philosopher gives those which signify the parts of such things as constitute the subject of this science. This is divided into two parts. In the first (445:C 906) he gives the various senses of the terms which signify the parts of unity; and in the second (467:C 954), those which signify the parts of being ("In one sense"). For substance, which is also posited as the subject of this science, is a single category which is not divided into many categories.
The first part is divided into two sections. In the first he gives the various senses of the terms which signify the parts of unity; and in the second (457:C 936), those which signify something that flows from the notion of unity, namely, prior and subsequent ("Things are said to be"). For to be one is to be a principle or starting point, as has been explained above (432:C 872).
907. The first part is divided into two sections. In the first he gives the various senses of the terms which signify the primary parts of unity and of its opposite, plurality; and in the second (451:C 922), he gives those which signify certain secondary parts of unity ("By opposites").
Now the parts of unity are sameness, which is oneness in substance; likeness, which is oneness in quality; and equality, which is oneness in quantity. And, opposed to these, the parts of plurality are otherness, unlikeness and inequality.
In regard to the first he does two things. First, he gives the various senses in which the term same is used, and the senses of its opposite. Second (449:C q18), he gives the various senses of the term like, and of its opposite, unlike ("Things are said to be like"). He makes no mention here, however, of the term equal and its opposite, because in the case of these terms plurality is not so evident.
In regard to the first part he does three things. First, he gives the various senses of the term same; second (447:C 91D, of the term other, or diverse ("Those things are said to be other"); and third (448:C 916), of the term different ("Things are said to be different").
In regard to the first he does two things. First, he gives the ways in which things are said to be accidentally the same; and second (446:C 911), he gives those in which things are said to be essentially the same ("And others").
The “same”, “per accidens” & “per se”
908. He says that things are said to be accidentally the same (idem per accidens) in three ways. (1) In one way they are the same in the sense that two accidents are; thus “white” and “musical” are said to be the same because they are accidents of the same subject. (2) Things are accidentally the same in a second way when a predicate is said to be the same as a subject inasmuch as it is predicated of it; thus when it is said that the man is musical, these (man and musical) are said to be the same because musical is an accident of a man, i.e., the predicate is an accident of the subject. (3) And things are accidentally the same in a third way when the subject is said to be the same as an accident inasmuch as it is predicated of it. For example, when it is said that the musical thing is a man, it is understood that the man is the same as the musical thing; for what is predicated of some subject is identified with that subject. And sameness in this sense means that the subject is an accident of the predicate.
909. Now besides these ways in which things are accidentally the same, in which an accident and a subject are taken in themselves, there are also others, i.e., those in which an accident is taken in conjunction with a subject. And when this occurs two senses of the term same have to be distinguished. (1) One of these is signified when an accident taken singly is predicated of the composite of subject and accident; and then the meaning is that the accident is the same as both of the simple terms taken together; for example, “musical” is the same as “musical man.” (2) The other is signified when the composite of accident and subject is predicated of the subject taken singly, as when we say that the man is a musical man; and then both of these (the composite “musical man”) are signified as being the same as this, i.e., as the subject taken singly. The same notion applies if an accident is taken singly and a subject is taken in combination with the accident. This would be the case, for example, if we were to say that what is musical is a musical man, or the reverse, for both “man” and “musical” are said to be accidentally the same as “musical man,” which is the composite, when these two are predicated of that one thing, and vice versa.
910. From this he draws the further conclusion that, in all of the foregoing modes of predication in which things are said to be accidentally the same, no term is predicated universally. For it is not true to say that every man is the same as what is musical. This becomes clear as follows: Only those attributes which belong essentially to the same subject are predicated universally of universals; for a predicate is predicated essentially of a subject because the mode of predication, which is a universal one, agrees with the condition of the subject, which is universal. However, accidents are not predicated essentially of universals, but only by reason of singular things; and thus they are not predicated universally of universals. But while accidents are predicated in an unqualified sense of singular things (for Socrates and musical Socrates seem to be the same in subject), they are not predicated universally of singular things; for nothing can be predicated universally of something that is not universal. But Socrates is not universal, because he is not present in many. Hence nothing can be predicated of Socrates so that we should say “every Socrates” as we say “every man.” The things of which we have spoken, then, are said to be one in this way, i.e., accidentally, as has been stated.
911. And others (446).
Then he gives the ways in which things are said to be essentially the same (idem per se). He says that things are said to be essentially the same in the same number of ways in which they are said to be essentially one. Now all of the ways in which things are said to be essentially one are reduced to two. (1) Thus, in one sense, things are said to be essentially one because their matter is one, whether we take the matter to be the same in species or in number. The second and third ways in which things are one are reduced to this. (2) And, in another sense, things are said to be one because their substance is one, whether by reason of continuity, which pertains to the first way in which things are one, or by reason of the unity and indivisibility of their intelligible structure, which pertains to the fourth and fifth ways. Therefore some things are said to be the same in these ways too.
912. From this he further concludes that sameness (identitas) is a unity or union. For things which are said to be the same are either many in being, but are said to be the same inasmuch as they agree in some respect, or they are one in being, but the intellect uses this as many in order to understand a relationship; for a relationship can be understood only between two extremes. This is what happens, for example, when we say that something is the same as itself; for the intellect then uses something which is one in reality as though it were two, otherwise it could not designate the relationship of a thing to itself. Hence it is clear that, if a relationship always requires two extremes, and in relations of this kind there are not two extremes in reality but only in the mind, then the relationship of sameness according to which something is said to be absolutely the same, will not be a real relation but only a conceptual relation. This is not the case, however, when any two things are said to be the same either in genus or in species. For if the relationship of sameness were something in addition to what we designate by the term same, then since this reality, which is a relation, is the same as itself, it would have to have for a like reason something that is also the same as itself; and so on to infinity. Now while it is impossible to proceed to infinity in the case of real beings, nothing prevents this from taking place in the case of things which have being in the mind. For since the mind may reflect on its own act it can understand that it understands; and it can also understand this act in turn, and so on to infinity.

LESSON 12
Various Senses of Diverse, Different, Like, Contrary, and Diverse in Species
ARISTOTLE'S TEXT Chapters 9 & 10: 1018a 9-1018b 8
447. Things are said to be other or diverse (diversa) of which either the forms or the matter or the intelligible structure of the essence is many; and in general the term other has senses opposite to those of the same.
448. Things are said to be different (differentia) which, while being diverse, are the same in some respect, and not merely in number, but in species or in genus or proportionally. And so also are those things whose genus is not the same, and contraries, and all those things which have diversity or otherness in their essence.
449. Things are said to be like (similia) which undergo the same modifications; or undergo more of the same than of different modifications; or whose quality is one.
450. And whatever has a greater number or the more important of those contraries in reference to which alteration is possible is said to be like something else. And things are said to be unlike (dissimilia) in ways opposite to those in which they are like.
Chapter 10
451. By opposites (opposita) we mean contraries, contradictories, relatives, and privation and possession.

452. And opposites also mean the ultimate parts of which things are composed and into which they are dissolved, as in processes of generation and corruption. And those things which cannot be present at the same time in a subject which is receptive of them are called opposites: either they themselves or the things of which they are composed. Gray and white, for example, are not present at the same time in the same subject, and therefore the things of which they are composed are opposites.
453. By contraries (contraria) we mean those attributes which, differing in genus, cannot be present at the same time in the same subject; and also those which differ most in the same genus; and those which differ most in the same subject; and those which differ most among those which come under the same power; and things which differ most either absolutely or in genus or in species.
454. Other things are called contraries either because they have contrary attributes or because they are receptive of them; and others because they are capable of causing them or undergoing them, or because they are actually causing them or undergoing them, or because they are rejections or acquisitions or possessions or privations of such attributes.
455. But since the term being and the term one are used in many ways, all other terms which are used in relation to them must follow upon them; so that the terms same, diverse and contrary vary according to each category.
456. Those things are said to he diverse (or other) in species which belong to the same genus but are not subalternate. And so are those which belong to the same genus and have a difference; and also those which have contrariety in their substance. For contraries differ from each other in species, either all of them, or those which are called such in a primary sense; and so are those things whose intelligible structures differ in the lowest species of the genus (for example, man and horse do not differ in genus but their intelligible structures are different); and those attributes which belong to the same substance and have a difference. Things which are the same in species are said to be such in ways opposite to to those just given.
COMMENTARY
Diverse
913. Here he explains the various ways in which the term diverse (or other) is used, and he gives three senses. (1) Thus some things are said to be diverse in species because their species are many, as an ass and an ox; (2) others are said to be diverse in number because their matters differ, as two individuals of one species; (3) and others are said to be diverse because “the intelligible structure of the essence,” i.e., the definition designating their substance, is different. For some things may be the same in number, i.e., from the viewpoint of matter, but diverse in their intelligible structure, as Socrates and this white man.
914. And since many modes of diversity can be considered (for example, diversity in genus, and the diversity resulting from the division of the continuous), he therefore adds that the term diverse means the very opposite of the same; for to every way in which things are the same there corresponds an opposite way in which they are diverse. Hence things are said to be diverse in the same number of senses in which they are said to be the same.
915. Yet the other ways in which things are said to be one, i.e., the same, can be reduced to those stated here. For diversity of genus is included in diversity of species, and diversity of quantity is included in diversity of matter, because the parts of a quantity have the character of matter in relation to the whole.
Different
916. Things are said to be “different” (448).
Then he gives the various senses in which the term different is used, and there are two of them. First, any two things are said properly to be different which, while being diverse, are “the same in some respect,” i.e., they have some one thing in common. And this is so (1) whether they have some one thing in common numerically, as Socrates sitting and Socrates not sitting; or (2) whether they have some one thing in common specifically, as Socrates and Plato have man in common; or (3) whether they have a common genus, as man and ass share in the genus animal; or (4) whether they share in some one thing proportionally, as quantity and quality both share in being. And from this it is evident that everything different is diverse, but not the reverse. For diverse things which agree in no respect cannot properly be called different, because they do not differ in some other respect but only in themselves; but that is said to be different which differs in some particular respect.
The term different is used in a second way when it is taken commonly in place of the term diverse; and then those things are also said to be different which belong to diverse genera and have nothing in common.
917. Next he indicates the kind of things which admit of difference in the first way, which is the proper one. Now those things which are said properly to differ must agree in some respect. Those which agree in species differ only by accidental differences; for example, Socrates insofar as he is white or just differs from Plato insofar as he is black or musical. And those things which agree in genus and are diverse in species differ by substantial differences. And since this is so, then those things are said to differ most properly which are the same in genus and diverse in species. For (+) every genus is divided into contrary differences, but (-) not every genus is divided into contrary species. Thus the species of color, white and black, are contraries, and so are their differences, expanding and contracting. And the differences of animal, rational and irrational, are contraries; but the species of animal, such as man, horse, and the like, are not.
Therefore things which are said to differ most properly are either those which are contrary species, as white and black, or those species of one genus which are not contrary but have contrariety in their essence because of the contrariety of differences which belong to the essence of the species.
Similar
918. Things are said to be “like” (449).
Here he points out the various ways in which the term like is used, and in regard to this he does two things. First, he indicates the various ways in which this term is used; and second (922), he gives those senses in which the term unlike is used (“By opposites”).
In regard to the first he does two things. First, he gives the ways in which the term like is used; and second (920), he explains how one thing is said to be most like another (“And whatever”).
He gives three ways in which things are like. Now it is evident that oneness in quality causes likeness. Further, undergoing or affection (passio) is associated with quality, because undergoing is most noticeable in the case of qualitative change or alteration; and thus one species of quality is called affection or possible quality. Hence things are observed to be like not only insofar as they have a common quality but also insofar as they undergo or suffer something in common. And this can be taken from two points of view: either from that of the affection or undergoing, or from that of the subject in which the affection is terminated.
919. Some things are like, then, for three reasons. (1) First, they undergo or suffer the same thing; for example, two pieces of wood which are consumed by fire can be said to be like. (2) Second, several things are like merely because they are affected or undergo something, whether this be the same or different; for example, two men, one of whom is beaten and the other imprisoned, are said to be like in that they both undergo something or suffer. (3) Third, those things are said to be like which have one quality; for example, two white things are alike in whiteness, and two stars in the heaven are alike in brightness or in power.
920. And whatever (450).
[ more or less ] Then he shows how one thing is said to be most like some other thing. For when there are several contraries of the sort which are observed to be alterable, whatever resembles some other thing in having the more important of these contraries is said to be more properly like that thing. For example, garlic, which is hot and dry, is said to be more properly like fire than sugar, which is hot and moist. The same holds true of any two things which are like some third thing in terms of only one quality; for whatever resembles some other thing in terms of some quality which is more proper to itself, is said to be more properly like that thing. For example, air is more properly like fire than earth; for air is like fire in reference to warmth, which is a quality proper to fire itself to a greater degree than dryness, in reference to which earth is like air.
Opposite
922. By “opposites” (451).
Here he distinguishes between the secondary parts of plurality, i.e., those contained under difference and diversity, which are its primary parts; and in regard to this he does three things. First, he gives the various ways in which the term opposite is used; second (925), those in which the term contrary is used (“By contraries”); and third (931), those in which things are said to be diverse or other in species (“Those things are said to be”).
In regard to the first he does two things. First (451), he gives the various ways in which we speak of opposites; and there are four of these: contradictories, contraries, privation and possession, and relatives. (1) For one thing is contraposed or opposed to another either by reason of dependence, i.e., insofar as one depends on another, and then they are opposed as relatives, or (2) by reason of removal, i.e., because one removes another. This occurs in three ways: (a) either one thing removes another entirely and leaves nothing, and then there is negation; or (b) the subject alone remains, and then there is privation; or the subject and genus remain, and then there is contrariety. For there are contraries not only in the same subject but also in the same genus.
923. And opposites (452).
Second, he gives two ways in which things can be recognized as opposites, (1) The first of these pertains to motion, for in any motion or change the terminus from which is the opposite of the terminus to which. Hence those things from which motion begins and those in which it ends are opposites. This is evident in processes of generation; for the white is generated from the not-white, and fire is generated from what is not-fire.
924. (2) The second pertains to the subject. For those attributes which cannot belong at the same time to the same subject must be the opposite of each other, either they themselves or the things in which they are present. For the same body cannot be at the same time both white and black, which are contraries; nor can the terms man and ass be predicated of the same thing, because their intelligible structures contain opposite differences, i.e., rational and irrational. The same holds true of gray and white, because gray is composed of black, which is the opposite of white. And we should note that he expressly says, “in the same subject”; for certain things cannot exist at the the same time in the same subject, not because they are opposed to each other, but because the subject is not receptive of the one or the other; for example, whiteness and music cannot exist at the same time in an ass, but they can exist at the same time in a man.
Contrary
925. By “contraries” (453).
Then he states the various ways in which the term contrary is used, and in regard to this he does three things.
First, he gives the principal ways in which things are said to be contrary. Among these he includes, first, one improper usage of the term, i.e., that whereby some attributes are called contraries which, while differing in genus, cannot belong at the same time to the same subject; for properly speaking contraries are attributes which belong to one genus. An example of this would be found if we were to say that heaviness and circular motion cannot belong to the same subject.
926. Then he gives a second usage of the term, which is a proper one, according to which contraries are said to be things that agree in some respect; for contraries agree in three respects, namely, in reference to the same genus, or to the same subject, or to the same power. Then he uses these three to expose the things which are real contraries. He says (1) that those attributes which differ most in the same genus are called contraries, as white and black in the genus of color; (2) and those which differ most in the same subject, as health and disease in an animal; (3) and those which differ most in reference to the same power, as what is correct and what is incorrect in reference to grammar; for rational powers extend to opposites. He says “most” in order to differentiate contraries from the intermediate attributes which lie between them, which also agree in the same genus, subject and power, yet do not differ to the greatest degree.
927. [ e.g. ] Hence he adds the universal notion involved in things which are designated as contraries, namely, that contraries are things which differ most either absolutely or in the same genus or in the same species. They differ “absolutely,” for example, in the case of local motion, where the extremes are separated most widely, as the most easterly and westerly points of the whole universe, which are the limits of its diameter. And they differ “in the same genus,” as the specific differences which divide a genus; and “in the same species,” as contrary differences of an accidental kind by which individuals of the same species differ from each other.
928. [ e.g. ] Here he shows in what respect some things are said to be contraries in a secondary way because they are related to those things which are contraries in the primary way. For some things are contraries either because they actually possess contraries, as fire and water are called contraries because one is hot and the other cold; or because they are the potential recipients of contraries, as what is receptive of health and of disease; or because they are potentially causing contraries or undergoing them, as what is capable of heating and of cooling, and what is able to be heated and to be cooled; or because they are actually causing contraries or undergoing them, as what is heating and cooling or being heated and being cooled; or because they are expulsions or rejections or acquisitions of contraries, or even possessions or privations of them. For the privation of white is the opposite of the privation of black, just as the possession of the former is the opposite of that of the latter.
929. It is evident, then, that he touches on a threefold relationship of contraries to things: (1) one is to a subject which is either in act or in potency; (2) another is to something that is active or passive in act or in potency; and (3) a third is to processes of generation and corruption, either to the processes themselves or to their termini, which are possession and privation.
930. But since the term (455).
He gives a third way in which the term contrary is used, and he also shows why the foregoing terms are used in many ways. For since the terms one and being have several meanings, the terms which are based upon them must also have several meanings; for example, same and diverse, which flow from one and many; and contrary, which is contained under diverse. Hence diverse must be divided according to the ten categories just as being and one are.
Diverse in species
931. Those things (456).
He now explains the various ways in which things are said to be diverse (or other) in species, and he gives five of these.
First, they belong to the same genus and are not subalternate; for example, science and whiteness both come under quality, yet they are not distinguished from each other by opposite differences.
932. Second, they belong to the same genus and are distinguished from each other by some difference, whether such differences are contrary or not, as two-footed and four-footed.
933. Third, their subjects contain contrariety; i.e., those things which are distinguished by contrary differences, whether the subjects are contrary themselves (as white and black, which are distinguished by the differences “expanding” and “contracting”) or not (as man and ass, which are distinguished by the differences “rational” and “irrational”). For contraries must differ in species, either all of them, or those which are called contraries in the primary sense.
934. Fourth, the lowest species are diverse and are the last in some genus, as man and horse. For those things which differ only in species are said more properly to differ in species than those which differ both in species and in genus.
935. Fifth, they are accidents in the same subject, yet differ from each other; for many accidents of one and the same kind cannot exist in the same subject. And things are said to be the same in species in ways opposite to those given above.

LESSON 13
The Ways in Which Things Are Prior and Subsequent
ARISTOTLE'S TEXT Chapter 11: 1018b 9-1019a 14
457. Things are said to be prior and subsequent insofar as there is some primary thing or principle in each class; for prior means what is nearer to some principle determined either in an absolute sense and by nature, or relatively, or in reference to place, or in certain other ways.
458. For example, a thing is prior in place because it is nearer either to some naturally determined place, as the middle or last, or to one that depends on chance. And what is farther away is subsequent.
459. Other things are prior in time. For some are prior because they are farther away from the present, as in the case of things which have taken place. Thus the Trojan war is prior to that of the Medes because it is farther away from the present. And others are prior in time because they are nearer to the present, as in the case of future events; for the Nemean [games] are prior to the Pythian because they are nearer to the present, provided that the present is taken as the principle or primary point.
460. Other things are prior in motion; for what is nearer to a first mover is prior; for example, the boy is prior to the man. And this too is a kind of principle in an absolute sense. Other things are prior in power; for whatever surpasses another in power, or is more powerful, is prior. And such is that according to whose will another, i.e., a subsequent, thing necessarily follows, because if the one does not move, the other is not moved, and if it does move, the other is moved; and will is a principle.
461. Other things are prior in arrangement, and these are the things which have a different place in relation to some one determinate thing according to some plan; for example, one who stands second is prior to one who stands third; and among the strings of the lyre the paranete is prior to the nete. For in the one case it is [the leader] who is taken as the principle or starting point; and in the other it is the middle string. These things, then, are said to be prior in this way.
462. In another way, whatever is prior in knowledge is considered to be prior in an absolute sense. And of such things some are prior in a different way, for some are prior in reference to reason, and others in reference to the senses. For universals are prior in reference to reason, but singulars in reference to the senses.
463. And in the intelligible structure the attribute is prior to the whole, as,'musical" is prior to "musical man." For the intelligible structure is not complete without one of its parts, and "musical man" cannot exist unless there is someone who is musical.
464. Again, the attributes of prior things are said to be prior, as straightness is prior to smoothness; for the former is a property of a line considered in itself, and the latter a property of surface. Some things, then, are said to be prior and subsequent in this way.
465. But others are said to be prior in nature and in substance, namely, all those things which can exist without others, although others cannot exist without them; and this is the division which Plato used. And since the term being is used in many ways, the first subject is prior, and therefore substance is prior. And things which exist potentially and those which exist actually are prior in various ways. For some things are prior in being potential, and others in being actual; for example, potentially half a line is prior to the entire line, and a part is prior to the whole, and matter is prior to substance. But in reference to actuality they are subsequent; for when the whole has been dissolved into such parts they will exist actually.
466. In a sense, then, all things which are prior and subsequent are said to be such in this [last] way. For some things can exist without others so far as the process of generation is concerned (as the whole without the parts), and some again without others so far as the process of corruption is concerned (as the parts without the whole). The same thing applies in other cases.
COMMENTARY
Prior & posterior
936. Having given the various senses of the terms which signify the parts of unity, here Aristotle gives those which signify order, namely, prior and subsequent. For unity implies a certain order, because the essence of unity consists in being a principle, as was stated above (872). In regard to the first he does two things. First, he indicates the common meaning of the terms prior and subsequent; and second (936), he gives the various senses in which these terms are commonly taken (“For example, a thing”).
He accordingly says, first, that the meaning of the term prior depends on that of the term principle (or starting point); for the principle in each class of things is what is first in that class, and the term prior means what is nearest to some determinate principle. Now the relationship between a principle of this kind and something which is near it can be considered from several points of view. For something is a principle or primary thing either in an absolute sense and by nature (as a father is a principle of a child), or “relatively,” i.e., in relation to some extrinsic thing (for example, something that is subsequent by nature is said to be prior in relation to something else). Things which are prior in this last sense are such either in reference to knowledge or to perfection or to dignity, or in some such way. Or a thing is also said to be a principle and to be prior in reference to place; or even in certain other ways.
937. Then he gives the various ways in which things are said to be prior and subsequent. And since the terms prior and subsequent are used in reference to some principle, and a principle is what is first either in being or in becoming or in knowledge (as has been stated above 1404:C 761]), this part is therefore divided into three sections.
In the first he explains how a thing is said to be prior in motion and in quantity, because the order found in motion flows from that found in quantity. For the prior and subsequent in motion depends on the prior and subsequent in continuous quantity, as is stated in Book IV of the Physics. Second (946), he shows how one thing is said to be prior to another in knowledge (“In another way”). Third (950), he explains how one thing is said to be prior to another in being, i.e., in nature (“But others”).
In regard to the first he does two things. First, he shows how one thing is said to be prior and another subsequent in quantity in the case of continuous things; and second (944), how one thing is prior and another subsequent in the case of discrete things (“Other things are prior in arrangement”).
938. In treating the first member of this division he gives three ways in which things are prior.
(1) The first has to do with place; for example, a thing is said to be prior in place inasmuch as it is nearer to some determinate place, whether that place be the middle point in some continuous quantity or an extreme. For the center of the world, to which heavy bodies gravitate, can be taken as the principle (or starting point) of the order involving place, and then we put the elements in the following. order, saying that earth is first, water second, and so on. Or the outermost sphere can be taken as the principle, and then we say that fire is first, air second, and so on.
939. Now nearness to a principle of place, whatever it may be, can be taken in two ways: (a) in one way with reference to an order naturally determined, as water is naturally nearer to the middle of the universe than air, and air nearer to the extreme, i.e., the outermost sphere; (b) and in another way with reference to an order that depends “on chance,” i.e., insofar as some things have a certain order purely as a result of chance, or on some other cause than nature. For example, in the case of stones which lie on top of one another in a heap, the highest is prior according to one order, and the lowest according to another. And just as what is nearest to a principle is prior, in a similar way what is farther away from a principle is subsequent.
940. Other things are prior in time (459).
(2) Things are understood to be prior and subsequent in a second way with reference to the order in time. And he now describes this order, saying that other things are said to be prior in time, and this in various ways. For some things are prior because they are farther away from the present, as occurs “in the case of things which have taken place,” i.e., past events. For the Trojan wars are said to be prior to those of the Medes and the Persians (in which Xerxes, the king of the Persians and Medes, fought against the Greeks), because they are farther away from the present. And some things are said to be prior because they are closer or nearer to the present; for example, Meneleus is said to be prior to Pyrrho because he is nearer to some present moment in reference to which each was future. But this text seems to be false, because both of them lived before the time of Aristotle, when these words were written. And it is said in the Greek that the Nemean are prior to the Pythian, these being two holidays or feasts one of which was nearer to the moment at which these words were written although both were future.
941. Now it is clear that in this case we are using the present as a principle or starting point in time, because we say that something is prior or subsequent on the grounds that it is nearer to or farther away from the present. And those who hold that time is eternal must say this; for, when this is supposed, the only principle or starting point of time which can be taken is one that relates to some present moment, which is the middle point between the past and the future, inasmuch as time might proceed to infinity in both directions.
942. Other thins are prior in motion (460).
(3) The term prior is used in a third way with reference to the order in motion; and (a) he first shows how this applies to natural things. He says that some things are said to be prior in the order found in motion; for what is nearer to a first cause of motion is prior. A boy, for example, is prior to a man because he is nearer to his primary mover, i.e., the one begetting him. And the latter is also said to be prior because of his nearness to some principle. For that—the one moving and begetting—is in a sense a principle, though not in just any way at all (as happened in the case of place), but in an absolute sense and by nature. (b) Second, he also mentions this order of motion in the realm of the voluntary, saying that some things are said to be prior in power, as men who are placed in positions of authority. For one who surpasses another in power, or is more powerful, is said to be prior. This is the order of dignity.
943. Now it is evident that this order also involves motion; for one who is more powerful, or surpasses another in power, is one “according to whose will,” i.e., intention, something necessarily follows, because it is through him that some subsequent thing is put in motion. Hence, when the more powerful or prior does not move, no subsequent thing moves; but when the former moves, the latter is also moved. This is the position of a prince in a state; for it is by his authority that others are moved to carry out the things which he commands, and if he does not command them they do not move. And it is clear that the term prior is used here too because of the nearness of a thing to some principle. For “the will,” i.e., the intention, of the ruler is taken here as a principle, and those who are nearer to the ruler, and therefore prior, are the ones through whom his commands are made known to his subjects.
944. Other things are prior in arrangement (461).
He now explains how a thing is prior in the order found among discrete things. He says that some things are said to be prior in order only because they (the associated things) have some kind of arrangement, and not because of continuity, as happened in the previous cases. And things of this kind have a different place in relation to some one determinate thing from a given point of view, as one who stands second and one who stands third —the one who stands second being prior to the one who stands third. By one who stands second is meant one who stands next to someone, such as a king; and by one who stands third is meant one who stands third from the king. Hence another text reads, “The leader is prior to the one who stands third.” It is evident, then, that things are understood to have different places inasmuch as one is second and another third. And in a similar way the paranete is prior to the nete; for among the strings of the lyre the low-pitched string is called the hypate; the high-pitched, the nete; and the middle, the mese. And the paranete refers to that which is next to the nete and nearer to the mese.
945. It is also evident that something is said to be prior here because of its nearness to some principle, although this happens differently in both of the examples given above. For in the former case—that of one who stands second and one who stands third—the thing which is taken as a principle is a real starting point and extreme, namely, the one who is highest among them, or the chief of the others, as a king or some other person of this kind. But in the case of the strings of the lyre it is the middle one, i.e., the middle string, termed the mese, that is taken as the principle; and since those which are nearer to this are called the paranete, the paranete are therefore said to be prior to the nete. These things are said to be prior in this way, then, i.e., by the order in quantity, whether continuous or discrete.
946. In another way (462).
Here he shows how one thing is said to be prior to another in knowledge. Now what is prior in knowledge is also prior in an absolute sense and not in a qualified one, as was the case with place; for a thing is known through its principles. But since knowledge is twofold: intellectual or rational, and sensory, we say that things are prior in one way in reference to reason, and in another in reference to the senses.
947. He gives three ways in which something is prior in reference to reason or intellectual knowledge:
(1) First, there is the way in which universals are prior to singulars, although the opposite occurs in the case of sensory knowledge because there singulars are prior. For reason has to do with universals and the senses with singulars; and thus the senses know universals only accidentally inasmuch as they know the singular of which the universals are predicated. For a sense knows man inasmuch as it knows Socrates, who is a man; and in the opposite way the intellect knows Socrates inasmuch as it knows man. But what is essential is always prior to what is accidental.
948. And in the intelligible structure (463).
(2) Here he gives the second way in which a thing is prior in reference to reason. He says that in the intelligible structure “the attribute is prior to the whole,” i.e., to the composite of subject and attribute; thus “musical man” cannot be known without grasping the meaning of the part “musical.” And in the same way all other simple things are prior in intelligibility to the composite, although the opposite is true from the viewpoint of the senses; for it is composite things which are first offered to the senses.
949. Again, the attributes (464).
(3) Then he gives the third way. He says that the attributes of prior things are also said to be prior from the viewpoint of reason, as straightness is said to be prior to smoothness. For straightness is an essential property of a line, and smoothness a property of surface, and a line is naturally prior to surface. But from the viewpoint of the senses surface is prior to a line, and the attributes of composite things are prior to those of simple ones. These things, then, are said to be prior in this way, namely, according to the order in knowing.
950. But others (465).
He then gives the ways in which a thing is said to be prior according to the order in being, and in regard to this he does two things. First, he gives three ways in which a thing is said to be prior in being; and second (953), he reduces them to one (“In a sense, then”).
He says, first, that some things are said to be prior in being, i.e., “in nature and substance,” or according to the natural order in being. And this is so for three reasons:
(1) First, priority is attributed because of community or dependence; and according to this those things are said to be prior which can exist without others, although others cannot exist without them. And one thing is prior to another when the sequence of their being cannot be reversed, as is stated in the Categories. “This is the division,” i.e., the mode of division of prior and subsequent, which Plato used against others; for it was because of community or dependence that he wanted universals to be prior in being to singular things, surfaces prior to bodies, lines to surfaces, and numbers to all other things.
951. (2) Second, things are said to be prior in being because of the relationship of substance to accident. For since the term being is used in many senses and not univocally, all senses of being must be reduced to one primary sense, according to which being is said to be the subject of other things and to subsist of itself. Hence the first subject is said to be prior; and thus substance is prior to accident.
952. Third, things are said to be prior in being inasmuch as being is divided into the actual and the potential. For a thing is said to be prior in one way potentially and in another actually. A thing is said to be prior potentially in the sense that half a line is prior to an entire line, and any part to its whole, and matter “to substance,” i.e., to form. For all of the first things mentioned in these instances are related to the others, to which they are said to be prior, as something potential to something actual. However, from the viewpoint of actuality the first things mentioned are said to be subsequent, since they become actual only by the dissolution of some whole. For when a whole is dissolved into its parts, the parts then begin to exist actually.
953. In a sense, then (466).
Here he concludes that all of the ways in which the terms prior and subsequent are used can be reduced to the last one given; and especially to the first of these inasmuch as the term prior means something which can exist without other things, but not the reverse. For from the viewpoint of generation some things can exist without others, and it is in this way that a whole is prior to its parts; for when a whole has been generated its parts do not exist actually but only potentially. And from the viewpoint of corruption some things can exist without others; for example, the parts can exist without the whole after the whole has been corrupted and dissolved into its parts. And in the same way too the other senses of prior and subsequent can be reduced to this sense. For it is certain that prior things do not depend upon subsequent ones, but the reverse. Hence all prior things can exist without subsequent ones, but not the reverse.

LESSON 14
Various Senses of the Terms Potency, Capable, Incapable, Possible and Impossible
ARISTOTLE'S TEXT Chapter 12: 1019a 15-1020a 6
467. In one sense the term potency or power (potestas) means the principle of motion or change in some other thing as other; for example, the art of building is a potency which is not present in the thing built; but the art of medicine is a potency and is present in the one healed, but not inasmuch as he is healed. In general, then, potency means the principle of change or motion in some other thing as other.
468. Or it means the principle of a thing's being moved or changed by some other thing as other. For by reason of that principle by which a patient undergoes some change we sometimes say that it has the potency of undergoing if it is possible for it to undergo any change at all. But sometimes we do not say this by reason of every change which a thing can undergo but only if the change is for the better.
469. And in another sense potency means the ability or power to do this particular thing well or according to intention. For sometimes we say of those who can merely walk or talk but not well or as they planned, that they cannot walk or talk. And the same applies to things which are undergoing change.
470. Further, all states in virtue of which things are altogether unsusceptible to change or immutable, or are not easily changed for the worse, are called potencies or powers. For things are broken and crushed and bent and in general destroyed, not because they have a potency, but because they do not have one and are deficient in some way. And things are not susceptible to such processes when they are hardly or slightly affected by them because they have the potency and the ability to be in some definite state.
471. And since the term potency is used in these senses, the term capable or potent (possibilis) will be used in the same number of senses. Thus in one sense whatever has [within itself] the source of the motion or change which takes place in some other thing as other (for even something that brings another to rest is potent in a sense) is said to be capable. And in another sense that which receives such a potency or power from it is said to be capable.
472. And in still another sense a thing is said to be capable if it has the potency of being changed in some way, whether for the worse or for the better. For anything which is corrupted seems to be capable of being corrupted, since it would not have been corrupted if it had been incapable of it. But as matters stand it already has a certain disposition and cause and principle to undergo such change. Hence sometimes a thing seems to be such (i.e., capable) because it has something, and sometimes because it is deprived of something.
473. But if privation is in a sense a having, all things will be capable or potent by having something. But being is used in two different senses. Hence a thing is capable both by having some privation and principle, and by having the privation of this, if it can have a privation.
474. And in another sense a thing is capable because there is no potency or power in some other thing as other which can corrupt it.
475. Again, all these things are capable either because they merely might happen to come into being or not, or because they might do so well. For this sort of potency or power is found in inanimate things such as instruments. For men say that one lyre can produce a sound, and that another cannot, if it does not have a good tone.
476. Incapacity (impotentia), on the other hand, is a privation of capacity, i.e., a kind of removal of such a principle as has been described, either altogether, or in the case of something which is naturally disposed to have it, or when it is already naturally disposed to have it and does not. For it is not in the same way that a boy, a man and an eunuch are said to be incapable of begetting.
477. Again, there is an incapacity corresponding to each kind of capacity, both to that which can merely produce motion, and to that which can produce it well.
478. And some things are said to be incapable according to this sense of incapacity, but others in a different sense, namely, as possible and impossible. Impossible means that of which the contrary is necessarily true; thus it is impossible that the diagonal of a square should be commensurable with a side, because such a statement is false of which the contrary is not only true but also necessarily so, i.e., that the diagonal is not commensurable. Therefore, that the diagonal is commensurable is not only false but necessarily false.
479. And the contrary of this, i.e., the possible, is when the contrary is not necessarily false. For example, it is possible that a man should be seated, because it is not necessarily false that he should not be seated. Hence the term possible means in one sense (as has been stated), whatever is not necessarily false; and in another sense, whatever is true; and in still another, whatever may be true.
480. And what is called "a power" in geometry is called such metaphorically. These senses of capable, then, do not refer to potency.
481. But those senses which do refer to potency are all used in reference to the one primary sense of potency, namely, a principle of change in some other thing inasmuch as it is other. And other things are said to be capable [in a passive sense], some because some other thing has such power over them, some because it does not, and some because it has it in a special way. The same applies to the term incapable. Hence the proper definition of the primary kind of potency will be: a principle of change in some other thing as other.
COMMENTARY
Potency/capacity
954. Having treated the various senses of the terms which signify the parts of unity, here Aristotle begins to treat those which signify the parts of being. He does this, first, according as being is divided by act and potency; and second (977), according as it is divided by the ten categories “ Quantity means”).
In regard to the first, he gives the various senses in which the term potency or power (potestas) is used. But he omits the term act, because he could explain its meaning adequately only if the nature of forms had been made clear first, and he will do this in Books VIII (1703) and IX (1823). Hence in Book IX he immediately settles the question about potency and act together.
This part, then, is divided into two members. In the first he explains the various senses in which the term potency is used; and in the second (975), he reduces all of them to one primary sense (“But those senses”).
In regard to the first he does two things. First, he gives the various senses in which the term potency is used; and second (967), the various senses in which the term incapacity is used (“Incapacity”).
In treating the first he does two things. First, he gives the senses in which the term potency is used; and second (961), those in which the term capable or potent is used (“And since the term”).
955. In dealing with the first part, then, he gives four senses in which the term potency or power is used:
First, potency means an [active] principle of motion or change in some other thing as other. For there is some principle of motion or change in the thing changed, namely, the matter, or some formal principle on which the motion depends, as upward or downward motion is a result of the forms of lightness or heaviness. But a principle of this kind cannot be designated as the active power on which this motion depends. For everything which is moved is moved by another; and a thing moves itself only by means of its parts inasmuch as one part moves another, as is proved in Book VIII of the Physics. Hence insofar as a potency is a principle of motion in that in which motion is found, it is not included under active power but under passive potency. For heaviness in earth is not a principle causing motion but rather one which causes it to be moved. Hence active power must be present some other thing than the one moved, for example, the power of building is not in the thing being built but rather in the builder. And while the art of medicine is an active power, because the physician heals by means of it, it may also be found in the one who is healed, not inasmuch as he is healed, but accidentally, i.e., inasmuch as the physician and the one who is healed happen to be the same. So therefore generally speaking potency or power means in one sense a principle of motion or change in some other thing as other.
956. (2)Here he gives a second sense in which the term potency is used. He says that in another sense the term potency means the principle whereby something is moved or changed by another thing as other. Now this is passive potency, and it is by reason of it that a patient undergoes some change. For just as every agent or mover moves something other than itself and acts in something other than itself, so too every patient is acted upon by something other than itself, i.e., everything moved is moved by another. For that principle whereby one thing is properly moved or acted upon by another is called passive potency.
957. Now there are two ways in which we can say that a thing has the potency to be acted upon by another. Sometimes we attribute such a potency to something, whatever it may be, because it is able to undergo some change, whether it be good or bad. And sometimes we say that a thing has such a potency, not because it can undergo something evil, but because it can be changed for the better. For example, we do not say that one who can be overpowered has a potency [in this last sense], but we do attribute such a potency to one who can be taught or helped. And we speak thus because sometimes an ability to be changed for the worse is attributed to incapacity, and the ability not to be changed in the same way is attributed to potency, as will be said below (965).
958. Another text reads, “And sometimes this is not said of every change which a thing undergoes but of change to a contrary”; and this should be understood thus: whatever receives a perfection from something else is said in an improper sense to undergo a change; and it is in this sense that to understand is said to be a kind of undergoing. But that which receives along with a change in itself something other than what is natural to it is said in a proper sense to undergo a change. Hence such undergoing is also said to be a removing of something from a substance. But this can come about only by way of some contrary. Therefore, when a thing is acted upon in a way contrary to its own nature or condition, it is said in a proper sense to undergo a change or to be passive. And in this sense even illnesses are called undergoings. But when a thing receives something which is fitting to it by reason of its nature, it is said to be perfected rather than passive.
959. And in another sense (469).
(3) He now gives a third sense in which the term potency is used. He says that in another sense potency means the principle of performing some act, not in any way at all, but well or according to “intention,” i.e., according to what a man plans. For when men walk or talk but not well or as they planned to do, we say that they do not have the ability to walk or to talk. And “the same thing applies when things are being acted upon,” for a thing is said to be able to undergo something if it can undergo it well; for example, some pieces of wood are said to be combustible because they can be burned easily, and others are said to be incombustible because they cannot be burned easily.
960. Further, all states (470).
(4) He gives a fourth sense in which the term potency is used. He says that we designate as potencies all habits or forms or dispositions by which some things are said or made to be altogether incapable of being acted upon or changed, or to be not easily changed for the worse. For when bodies are changed for the worse, as those which are broken or bent or crushed or destroyed in any way at all, this does not happen to them because of some ability or potency but rather because of some inability and the weakness of some principle which does not have the power of resisting the thing which destroys them. For a thing is destroyed only because of the victory which the destroyer wins over it, and this is a result of the weakness of its proper active power. For those things which cannot be affected by defects of this kind, or can “hardly or only gradually” be affected by them (i.e., they are affected slowly or to a small degree) are such “because they have the potency and the ability to be in some definite state”; i.e., they have a certain perfection which prevents them from being overcome by contraries. And, as is said in the Categories, it is in this way that hard or healthy signifies a natural power which a thing has of resisting change by destructive agents. But soft and sickly signify incapacity or lack of power.
961. And since the term (471).
Here he gives the senses of the term capable or potent, which correspond to the above senses of potency. And there are two senses of capable which correspond to the first sense of potency.
(1) For according to its active power a thing is said to be capable of acting in two ways: in one way, because it acts immediately of itself; and in another way, because it acts through something else to which it communicates its power, as a king acts through a bailiff.
Hence he says that, since the term potency is used in this number of senses, the term capable or potent must also be used in the same number of senses. Thus in one sense it means something which has an active principle of change in itself, as what brings another to rest or to a stop”; i.e., what causes some other thing to stand still is said to be capable of bringing something different from itself to a state of rest. And it is used in another sense when a thing does not act directly but another thing receives such power from it that it can act directly.
962. And in still another (472).
(2) Next, he gives a second sense in which the term capable is used, and this corresponds to the second sense of the term potency, i.e., passive potency. He says that, in a different way from the foregoing, a thing said to be capable or potent when it can be changed in some respect, whatever it may be, i.e., whether it can be changed for the better or for the worse. And in this sense a thing is said to be corruptible because “it is capable of being corrupted,” which is to undergo change for the worse, or it is not corruptible because it is capable of not being corrupted, assuming that it is impossible for it to be corrupted.
963. And what is capable of being acted upon in some way must have within itself a certain disposition which is the cause and principle of its passivity, and this principle is called passive potency. But such a principle can be present in the thing acted upon for two reasons. First, this is because it possesses something; for example, a man is capable of suffering from some disease because he has an excessive amount of some inordinate humor. Second, a thing is capable of being acted upon because it lacks something which could resist the change. This is the case, for example, when a man is said to be capable of suffering from some disease because his strength and natural power have been weakened. Now both of these must be present in anything which is capable of being acted upon; for a thing would never be acted upon unless it both contained a subject which could receive the disposition or form induced in it as a result of the change and also lacked the power of resisting the action of an agent.
964. Now these two ways in which the principle of passivity is spoken of can be reduced to one, because privation can be designated as “ a having.” Thus it follows that to lack something is to have a privation, and so each way will involve the having of something. Now the designation of privation as a having and as something had follows from the fact that being is used in two different ways; and both privation and negation are called being in one of these ways, as has been pointed out at the beginning of Book IV (564). Hence it follows that negation and privation can also be designated as “havings.” We can say, then, that in general something is capable of undergoing because it contains a kind of “having” and a certain principle that enables it to be acted upon; for even to lack something is to have something, if a thing can have a privation.
965. An in another sense (474).
(3) Here he gives a third sense in which the term capable is used; and this sense corresponds to the fourth sense of potency inasmuch as a potency was said to be present in something which cannot be corrupted or changed for the worse. Thus he says that in another sense a thing is said to be capable because it does not have some potency or principle which enables it to be corrupted. And I mean by some other thing as other. For a thing is said to be potent or powerful in the sense that it cannot be overcome by something external so as to be corrupted.
966. Again, all these (475).
(4) He gives a fourth sense in which the term capable is used, and this corresponds to the third sense of potency inasmuch as potency designated the ability to act or be acted upon well. He says that according to the foregoing senses of potency which pertain both to acting and to being acted upon, a thing can be said to be capable either because it merely happens to come into being or not or because it happens to come into being well. For a thing is said to be capable of acting either because it can simply act or because it can act well and easily. And in a similar way a thing is said to be capable of being acted upon and corrupted because it can be acted upon easily. And this sense of potency is also found in inanimate things “such as instruments,” i.e., in the case of the lyre and other musical instruments. For one lyre is said to be able to produce a tone because it has a good tone, and another is said not to because its tone is not good.
Incapacity
967. Incapacity (476).
Then he gives the different senses of the term incapacity, and in regard to this he does two things. First, he gives the various senses in which we speak of incapacity; and second (970), he treats the different senses in which the term impossible is used (“And some things”).
In treating the first part he does two things. First, he gives the common meaning of the term incapacity. Second (969), he notes the various ways in which it is used (“Again, there is”).
He accordingly says, first, that incapacity is the privation of potency.
Now two things are required in the notion of privation, (1) and the first of these is the removal of an opposite state. But the opposite of incapacity is potency. Therefore, since potency is a kind of principle, incapacity will be the removal of that kind of principle which potency has been described to be. (2) The second thing required is that privation properly speaking must belong to a definite subject and at a definite time; and it is taken in an improper sense when taken without a definite subject and without a definite time. For properly speaking only that is said to be blind which is naturally fitted to have sight and at the time when it is naturally fitted to have it.
968. And he says that incapacity, such as it has been described, is the removal of a potency, (1) “either altogether,” i.e., universally, in the sense that every removal of a potency is called incapacity, whether the thing is naturally disposed to have the potency or not; or (2) it is the removal of a potency from something which is naturally fitted to have it at some time or other or only at the time when it is naturally fitted to have it. For incapacity is not taken in the same way when we say that a boy is incapable of begetting, and when we say this of a man and of an eunuch. For to say that a boy is incapable of begetting means that, while the subject is naturally fitted to beget, it cannot beget before the proper time. But to say that an eunuch is incapable of begetting means that, while he was naturally fitted to beget at the proper time, he cannot beget now; for he lacks the active principles of begetting. Hence incapacity here retains rather the notion of privation. But a mule or a stone is said to be incapable of begetting because neither can do so, and also because neither has any real aptitude for doing so.
969. Again, there is (477).
Then he explains the various senses of incapacity by contrasting them with the senses of potency. For just as potency is twofold, namely, active and passive, and both refer either to acting and being acted upon simply, or to acting and being acted upon well, in a similar fashion there is an opposite sense of incapacity corresponding to each type of potency. That is to say, there is a sense of incapacity corresponding “both to that which can merely produce motion and to that which can produce it well,” namely, to active potency, which is the potency to simply move a thing of to move it well, and to passive potency, which is the potency to simply be moved or to be moved well.
970. And some things (478).
Then he explains the various senses in which the term impossible is used; and in regard to this he does two things. First, he gives the various senses in which the term impossible is used; and then (975) he reduces them to one (“But those senses”). In regard to the first he does three things:
(1) First, he says that in one sense some things are said to be impossible because they have the foregoing incapacity which is opposed to potency. And impossible in this sense is used in four ways corresponding to those of incapacity.
971. (2) Accordingly, when he says “in a different sense, he gives another way in which some things are said to be impossible. And they are said to be such not because of the privation of some potency but because of the opposition existing between the terms in propositions. For since potency is referred to being, then just as being is predicated not only of things that exist in reality but also of the composition of a proposition inasmuch as it contains truth and falsity, in a similar fashion the terms possible and impossible are predicated not only of real potency and incapacity but also of the truth an falsity found in the combining or eparating of terms in propositions. ence the term impossible means that of which the contrary is necessarily true. For example, it is impossible that the diagonal of a square should be commensurable with a side, because such a statement is false whose contrary is not only true but necessarily so, namely, that it is not commensurable. Hence the statement that it is commensurable is necessarily false, and this is impossible.
972. And the contrary (479).
Here he shows that the possible is the opposite of the impossible in the second way mentioned; for the impossible is opposed to the possible in the second way mentioned. He says, then, that the possible, as the contrary of this second sense of the impossible, means that whose contrary is not necessarily false; for example, it is possible that a man should be seated, because the opposite of this—that he should not be seated—is not necessarily false.
973. From this it is clear that this sense of possible has three usages. (1) For in one way it designates what is false but is not necessarily so; for example, it is possible that a man should be seated while he is not seated, because the opposite of this is not necessarily true. (2) In another way possible designates what is true but is not necessarily so because its opposite is not necessarily false, for example, that Socrates should be seated while he is seated. (3) And in a third way it means that, although a thing is not true now, it may be true later on.
974. And what is called a “power” (480).
He shows how the term power is used metaphorically. He says that in geometry the term power is used metaphorically. For in geometry the square of a line is called its power by reason of the following likeness, namely, that just as from something in potency something actual comes to be, in a similar way from multiplying a line by itself its square results. It would be the same if we were to say that the number three is capable of becoming the number nine, because from multiplying the number three by itself the number nine results; for three times three makes nine. And just as the term impossible taken in the second sense does not correspond to any incapacity, in a similar way the senses of the term possible which were given last do not correspond to any potency, but they are used figuratively or in the sense of the true and the false.
975. But those senses (481).
He now reduces all senses of capable and incapable to one primary sense. He says that those senses of the term capable or potent which correspond to potency all refer to one primary kind of potency—the first active potency which was described above (955) as the principle of change in some other thing as other; because all the other senses of capable or potent are referred to this kind of potency. For a thing is said to be capable by reason of the fact that some other thing has active power over it, and in this sense it is said to be capable according to passive potency. And some things are said to be capable because some other thing does not have power over them as those which said to be capable because they cannot be corrupted by external agents. And others are said to be capable because they have it “in some special way,” i.e., because they have the power or potency to act or be acted upon well or easily.
976. And just as all things which are said to be capable because of some potency are reduced to one primary potency, in a similar way all things which are said to be incapable because of some impotency are reduced to one primary incapacity, which is the opposite of the primary potency. It is clear, then, that the proper notion of potency in the primary sense is this: a principle of change in some other thing as other; and this is the notion of active potency or power.

LESSON 15
The Meaning of Quantity. Its Kinds. The Essentially and Accidentally Quantitative
ARISTOTLE'S TEXT Chapter 13: 1020a 7-1020a 32
482. Quantity [or the quantitative] means what is divisible into constituent parts, both or one of which is by nature a one and a particular thing.
483. Therefore plurality [or multitude] is a kind of quantity if it is numerable; and so also is magnitude [or continuous quantity] if it is measurable. Plurality means what is potentially divisible into non-continuous parts; and magnitude means what is divisible into continuous parts. Again, of the kinds of magnitude, what is continuous in one dimension is length; in two, breadth; and in three, depth. And of these, limited plurality is number; limited length, a line; limited breadth, a surface; and limited depth, a body [or solid].
484. Again, some things are said to be quantitative essentially and others accidentally; for example, a line is quantitative essentially, but the musical accidentally.
485. And of those things which are quantitative essentially, some are such by reason of their substance, as a line is quantitative quidditatively. For in the definition expressing its quiddity some kind of quantity is found. Others are properties and states of this kind of substance, as much and little, long and short, broad and narrow, deep and shallow, heavy and light, and the like. And large and small, and larger and smaller, whether they are spoken of essentially or in relation to each other, are properties of quantity. And these terms are also transferred to other things.
486. But of things which are quantitative accidentally, some are said to be such in the sense in which the musical and the white are quantitative, i.e., because the subject to which they belong is quantitative. Others are said to be quantitative in the sense in which motion and time are, for these too are said to be in a sense quantitative and continuous because the things of which they are the properties are divisible. And I mean not the thing which is moved, but the space through which it is moved. For since space is quantitative, motion is also quantitative; and through it, i.e., motion, time is also quantitative.
COMMENTARY
Quantity
977. Since being is divided not only into potency and actuality but also into the ten categories, having given the different senses of the term potency (954-60), the Philosopher begins here to give the different senses of the terms which designate the categories.
First, he considers the term quantity; and second (987), the term quality (“Quality means”). Third (1001), he gives the different meanings of the term relative (“Some things”). He omits the other categories because they are limited to one class of natural beings, as is especially evident of action and passion, and of place and time.
In regard to the first he does three things. First, he gives the meaning of quantity. He says that quantity means what is divisible into constituent parts. Now this is said to distinguish this kind of division from that of compounds. For a compound is dissolved into the elements, and these are not present in it actually but only virtually. Hence, in the latter case there is not just division of quantity, but there must also be some alteration by means of which a compound is dissolved into its elements. He adds that both or one of these constituents is by nature “a one,” that is, something which is pointed out. He says this in order to exclude the division of a thing into its essential parts, which are matter and form; for neither one of these is fitted by nature to be a particular thing of itself.
978. Therefore plurality (483).
Second, he gives the kinds of quantity; and of these there are two primary kinds: plurality or multitude, and magnitude or measure. And each of these has the character of something quantitative inasmuch as plurality is numerable and magnitude is measurable. For mensuration pertains properly to quantity. However, plurality is defined as what is divisible potentially into parts which are not continuous; and magnitude as what is divisible into parts which are continuous. Now this occurs in three ways, and therefore there are three kinds of magnitude. For if inagnitude is divisible into continuous parts in one dimension only, it will be length; if into two, width; and if into three, depth. Again, when plurality or multitude is limited, it is called number. And a limited length is called a line; a limited width, surface; and a limited depth, body. For if multitude were unlimited, number would not exist, because what is unlimited cannot be numbered. Similarly, if length were unlimited, a line would not exist, because a line is a measurable length (and this is why it is stated in the definition of a line that its extremities are two points). The same things holds true of surface and of body.
979. Again, some things (484).
Third, he gives the different ways in which things are quantitative; and in regard to this he does three things. First, he draws a distinction between what is essentially quantitative, as a line, and what is accidentally quantitative, as the musical.
980. And of those (485).
Second, he gives the different senses in which things are essentially quantitative, and there are two of these. For some things are said to be such after the manner of a substance or subject, as line, surface or number; for each of these is essentially quantitative because quantity is given in the definition of each. For a line is a limited quantity divisible in length. The same is true of the other dimensions.
981. And other things belong essentially to the genus of quantity and are signified after the manner of a state or property of such substance, i.e., of a line, which is essentially quantitative, or of other similar kinds of quantity. For example, much and little are signified as properties of number; long and short, as properties of a line; broad and narrow, as properties of surface; and high and low or deep, as properties of body. And the same is true of heavy and light according to the opinion of those who said that having many surfaces, or atoms, causes bodies to be heavy, and having few causes them to be light. But the truth of the matter is that heavy and light do not pertain to quantity but to quality, as he states below (993). The same thing is true of other such attributes as these.
982. There are also certain attributes which are common properties of any continuous quantity, as large and small, and larger and smaller, whether these are taken “essentially,” i.e., absolutely, or “in relation to each other,” its something is said to be large and small relatively, as is stated in the Categories. But these terms which signify the properties of quantity pure and simple are also transferred to other things besides quantities. For whiteness is said to be large and small, and so also are other accidents of this kind.
983. But it must be borne in mind that of all the accidents quantity is closest to substance. Hence some men think that quantities, such as line, number, surface and body are substances. For next to substance only quantity can be divided into distinctive parts. For whiteness cannot be divided, and therefore it cannot be understood to be individuated except by its subject. And it is for this reason that only in the genus of quantity are some things designated as subjects and others as properties.
984. But of things (486).
Then he gives the different senses in which things are said to be accidentally quantitative. These senses are two. (1) In one sense, things are said to be accidentally quantitative only because they are accidents of some quantity; for example, white and musical are said to be quantitative because they are accidents of a subject which is quantitative.
985. (2) In another sense, some things are said to be accidentally quantitative, not because of the subject in which they exist, but because they are divided quantitatively as a result of the division of some quantity; for example, motion and time (which are said to be quantitative and continuous because of the subjects to which they belong) are divisible and are themselves divided as a result of the division of the subjects to which they belong. For time is divisible and continuous because of motion, and motion is divisible because of magnitude—not because of the magnitude of the thing which is moved, but because of the magnitude of the space through which it is moved. For since that magnitude is quantitative, motion is also quantitative; and since motion is quantitative, it follows that time is quantitative. Hence these can be said to be quantitative not merely accidentally but rather subsequently, inasmuch as they receive quantitative division from something prior.
986. However, it must be noted that in the Categories the Philosopher held that time is essentially quantitative, while here he holds that it is accidentally quantitative. There he distinguished between the species of quantity from the viewpoint of the different kinds of measure. For time, which is an external measure, has the character of one kind of measure, and continuous quantity, which is an internal measure, has a different one. Hence in the Categories time is given as another species of quantity, whereas here he considers the species of quantity from the viewpoint of the being of quantity.
Therefore those things which only receive their quantitative being from something else he does not give here as species of quantity, but as things which are accidentally quantitative, as motion and time. But motion has no other manner of measure than time and magnitude. Hence neither in this work nor in the Categories does he give it as a species of quantity. Place, however, is given there as a species of quantity. But it is not given as such here because it has a different manner of measure, although not a different quantitative being.

LESSON 16
The Senses of Quality
ARISTOTLE'S TEXT Chapter 14: 1020a 33-1020b 25
487. Quality (the qualified or of what sort [ quale ]) means in one sense substantial difference; for example, How is man's quiddity qualified? as a two-footed animal. How is a horse's? as a four-footed animal. A circle's? as a figure which is non-angular; as if substantial difference were quality. In this one sense, then, quality (qualitas) means substantial difference.
488. In another sense the term applies to immobile things and to the objects of mathematics, as numbers are of a certain type (quales), for example, those which are compound, and not only those of one dimension but also those of which surface and solid are the counterpart (for there are numbers which are so many times so much and so many times so many times so much). And in general it means what is present in substance besides quantity. For the substance of each number is what it is once; for example, the substance of six is not two times three but six taken once, for six times one is six.
489. Again, all the modifications of substances which are moved, such as heat and cold, whiteness and blackness, heaviness and lightness, and any other attributes of this sort according to which the bodies of changing things are said to be altered, are called qualities.
490. Further, the term quality is used of virtue and vice, and in general of good and evil.
491. The senses of quality, then, come down to two; and one of these is more basic than the other. For the primary kind of quality is substantial difference. And the quality found in number is a part of this, for this is a substantial difference, but either of things which are not moved, or not of them insofar as they are moved. The others, however, are the modifications of things which are moved inasmuch as they are moved, and are the differences of motions. And virtue and vice are parts of these modifications, for they indicate clearly the differences of the motion or activity according to which things in motion act or are acted upon well or badly. For what is capable of being moved or of acting in this way is good, and what cannot do so but acts in a contrary way is bad. And good and bad signify quality especially in the case of living things, and especially in those which have the power of choice.
COMMENTARY
Quality
987. Here he gives the various senses in which the term quality is used, and in regard to this he does two things. First, he gives four senses of the term quality; and second (966), he reduces them to two (“The senses of quality”).
(1) He accordingly says, first, that the term quality is used in one sense as “ substantial difference,” i.e., the difference by which one thing is distinguished substantially from another and which is included in the definition of the substance. And for this reason it is said that a difference is predicated as a substantial qualification. For example, if one were to ask what sort of (quale) animal man is, we would answer that he is two-footed; and if one were to ask what sort of animal a horse is, we would answer that it is four-footed; and if one were to ask what sort of figure a circle is, we would answer that it is “non-angular,” i.e., without angles; as if a substantial difference were quality. In one sense, then, quality means substantial difference.,
988. Now Aristotle omits this sense of quality in the Categories because it is not contained under the category of quality,—which he deals with there. But here he is dealing with the meaning of the term quality.
989. In another sense (488).
(2) Here he gives a second sense in which the term quality is used. He says that the term quality or “qualified” is used in another sense insofar as immobile things and the objects of mathematics are said to be qualified in a certain way. For the objects of mathematics are abstracted from motion, as is stated in Book VI of this work (1161). Such objects are numbers and continuous quantities, and of both we use the term quality. Thus we say that surfaces are qualified as being square or triangular. And similarly numbers are said to be qualified as being compound. Those numbers are said to be compound which have some common number that measures them; for example, the number six and the number nine are measured by the number three, and are not merely referred to one as a common measure. But those which are measured by no common number other than one are called uncompounded or first in their proportion.
990. Numbers are also spoken of as having quality in a metaphor taken from surface and from “solid,” i.e., body. They are considered like a surface inasmuch as one number is multiplied by another, either by the same number or by a different one, as in the phrase “twice three” or “three times three.” And this is what he means by “so many times so much”; for something like one dimension is designated by saying “three,” and a sort of second dimension by saying “twice three” or “three times three.”
991. Numbers are considered like a solid when there is a twofold multiplication, either of the same number by itself, or of different numbers by one; as in the expression “three times three times three” or “two times three times two” or “two times three times four.” And this is what he means by “so many times so many times so much.” For we treat of three dimensions in a number in somewhat the same way as in a solid; and in this arrangement of litlinbers there is something which is treated as a substance, as three, or any other number that is multiplied by another. And there is something else which is treated as quantity, as the multiplication of one number by another or by itself. Thus when I say “twice three,” the number two is signified after the manner of a measuring quantity, and the number three after the manner of a substance. Therefore what belongs to the substance of number besides quantity itself, which is the substance of number, is called a quality of it, as what is meant in saying twice or three times.
992. Another text reads “according to quantity,” and then the substance of number is said to be the number itself expressed in an unqualified sense, as “three.” And insofar as we consider the quality of a quantity, this is designated by multiplying one number by another. The rest of the text agrees with this, saying that the substance of any number is what it is said to be once; for example, the substance of six is six taken once, and not three taken twice or two taken three times; and this pertains to its quality. For to speak of a number in terms of surface or solid, whether square or cubic,is to speak of its quality. And this type of quality is the fourth kind given in the Categories.
993. Again, all the modifications (489).
(3) Then he gives the third sense in which quality is used. He says that qualities also mean the modifications of mobile substances according to which bodies are changed through alteration, as heat and cold and accidents of this kind. And this sense of quality belongs to the third kind of quality given in the Categories.
994. (4) Next he gives the fourth sense in which quality is used. He says that quality or “qualified” is used in a fourth sense insofar as something is disposed by virtue or vice, or in whatever way it is well or badly disposed, as by knowledge or ignorance, health or sickness, and the like. This is the first kind of quality given in the Categories.
995. Now he omits the second of these senses of quality because it is contained rather under power, since it is signified only as a principle which resists modification. But it is given in the Categories among the kinds of quality because of the way in which it is named. However, according to its mode of being it is contained rather under power, as he also held above (960).
996. The senses of quality (491).
Then he reduces to two the four senses of quality so far given, saying that a thing is said to be qualified in a certain way in two senses, inasmuch as two of these four senses are reduced to the other two.
(1) The most basic of these senses is the first one, according to which quality means substantial difference, because by means of it a thing is designated as being informed and qualified.
997. The quality found in numbers and in other objects of mathematics is reduced to this as a part. For qualities of this kind are in a sense the substantial differences of mathematical objects, because they are signified after the manner of substance to a greater degree than the other accidents, as was stated in the chapter on quantity (980). Further, qualities of this kind constitute substantial differences, “either of things which are not moved, or not of them insofar as they are moved”; and he says this in order to show that it makes no difference to his thesis whether the objects of mathematics are self-subsistent substances, as Plato claimed, and are separate from motion; or whether they exist in substances which are mobile in reality but separate in thought. For in the first sense they would not be qualities of things which are moved; but in the second sense they would be, but not inasmuch as they are moved.
998. (2) The second basic sense in which quality is used is that in which the modifications of things which are moved as such, and also the differences of things which are moved, are called qualities. They are called the differences of motions because alterations differ in terms of such qualities, as becoming hot and becoming cold differ in terms of heat and cold.
999. The sense in which virtue and vice are called qualities is reduced to this last sense, for it is in a way a part of this sense. For virtue and vice indicate certain differences of motion and activity based on good or bad performance. For virtue is that by which a thing is well disposed to act or be acted upon, and vice is that by which a thing is badly disposed. The same is true of other habits, whether they are intellectual, as science, or corporal, as health.
1000. But the terms well and badly relate chiefly to quality in living things, and especially in those having “election,” i.e., choice. And this is true because good has the role of an end or goal. So those things which act by choice act for an end. Now to act for an end belongs particularly to living things. For non-living things act or are moved for an end, not inasmuch as they know the end, or inasmuch as they themselves act for an end, but rather inasmuch as they are directed by something else which gives them their natural inclination, just as an arrow, for example, is directed toward its goal by an archer. And non-rational living things apprehend an end or goal and desire it by an appetite of the soul, and they move locally toward some end or goal inasmuch as they have discernment of it; but their appetite for an end, and for those things which exist for the sake of the end, is determined for them by a natural inclination. Hence they are acted upon rather than act; and thus their judgment is not free. But rational beings, in whom alone choice exists, know both the end and the proportion of the means to the end. Therefore, just as they move themselves toward the end, so also do they move themselves to desire the end and the means; and for this reason they have free choice.

LESSON 17
The Senses of Relative
ARISTOTLE'S TEXT Chapter 15: 1020b 26-1021b 11
492. Some things are said to be relative (ad aliquid) directly, as double to half and triple to a third part; and in general what is multiplied to a part of what is multiplied, and what includes to what is included in it. And in another sense as what heats to what can be heated, and what cuts to what can be cut; and in general everything active to everything passive. And in another sense as what is measurable to a measure, and what is knowable to knowledge, and what is sensible to sense.
493. The first things which are said to be relative numerically are such, either without qualification, or in some definite relation to them, or to unity; as double is related to half as a definite number. And the multiple is related numerically to the unit, but not in a definite numerical relation such as this or that. But what is one and a half times as great as something else is related to it in a definite numerical relation to a number. And the superparticular is related to the subparticular in an indefinite relation, as what is multiple is related to a number. And what includes is related to what is included in it as something altogether indefinite in number, for number is commensurable. For what includes is related to what is included in it according to so much and something more; but this something more is indefinite. For whatever the case may be, it is either equal or not equal to it. Therefore all these relations are said to be numerical and are properties.of number.
494. Further, equal, like and same are said to be relative, but in a different way, because all these terms are referred to unity. For those things are the same whose substance is one; and those are alike whose quality is one; and those are equal whose quantity is one. And unity is the principle and measure of number. Hence all these are said to be relative numerically, yet not in the same way.
495. Active and passive things are relative in virtue of active and passive potencies and the operations of potencies; for example, what can heat is relative to what can be heated, because it can heat it; and what is heating is relative to what is being heated; and what is cutting to what is being cut, inasmuch as they are doing these things. But of those things which are relative numerically there are no operations, except in the sense stated elsewhere; and operations which imply motion are not found in them. Moreover, of things which are relative potentially, some are said to be relative temporally also, as what makes to what is made, and what will make to what will be made. For in this way a father is said to be the father of his son, because the former has acted, whereas the latter has been acted upon. Again, some things are said to be relative according to the privation of potency; for example, the incapable and other terms used in this way, as the invisible.
496. Therefore things which are said to be relative numerically and potentially are all relative because the subject of the reference is itself referred to something else, not because something else is referred to it. But what is measurable and knowable and thinkable are said to be relative because in each case something else is referred to them, not because they are referred to something else. For by what is thinkable is meant that of which there may be a thought. However, a thought is not relative to the one whose thought it is, for then the same thing would be expressed twice. And similarly sight is relative to that of which it is the sight and not to the one whose sight it is (although it is true to say this); but it is relative to color or to something of this sort. But then the same thing would be said twice, that sight is of the one whose sight it is. Things which are said to be relative directly, then, are spoken of in this way.
497. And other things are said to be relative because their genera are such; for example, medicine is relative because its genus, science, seems to be relative. Furthermore, of this type are all things which are said to be relative by reason of their subject; for example, equality is said to be relative because equal is relative; and likeness, because like is relative.
498. But other things are said to be relative indirectly, as man is relative because he happens to be double, and this is relative; or the white is said to be relative because the same thing happens to be white and double.
COMMENTARY
Relation
1001. Here the Philosopher establishes the meaning of the relative or relation; and in regard to this he does two things. First, he gives the senses in which things are said to be relative directly; and second (1030), those in which things are said to be relative indirectly (“And other things”).
In regard to the first he does two things. First, he enumerates the senses in which things are said to be relative directly. Second (1006), he proceeds to deal with these (“The first things”).
He accordingly gives, first, three senses in which things are said to be relative directly.
The first of these has to do with number and quantity as double to half and triple to a third, and “what is multiplied,” i.e., the multiple, to a part “of what is multiplied,” i.e., the submultiple, “and what includes to what is included in it.” But what includes is here taken for what is greater in quantity. For everything which is greater in quantity includes within itself that which it exceeds. For it is this and something more; for example, five includes within itself four, and three cubits include two.
1002. The second sense is that in which some things are said to be relative according to acting and undergoing, or to active and passive potency; for example, in the realm of natural actions, as what can heat to what can be heated; and in the realm of artificial actions, as what can cut to what can be cut; and in general as everything active to everything passive.
1003. The third sense of relation is that in which something measurable is said to be relative to a measure. Here measure and measurable are not taken (-) quantitatively (for this pertains to the first sense, in which either one is said to be relative to the other, since double is said to be relative to half and half to double), but (+) according to the measurement of being and truth. For the truth of knowledge is measured by the knowable object. For it is because a thing is so or is not so that a statement is known to be true or false, and not the reverse. The same thing applies in the case of a sensible object and sensation. And for this reason a measure and what is measurable are not said to be related to each other reciprocally, as in the other senses, but only what is measurable is related to its measure. And in a similar fashion too an image is related to that of which it is the image as what is measurable is related to its measure. For the truth of an image is measured by the thing whose image it is.
1004. These senses are explained as follows: since a real relation consists in the bearing of one thing upon another, there must be as many relations of this kind as there are ways in which one thing can bear upon another. (3) Now one thing bears upon another either in being, inasmuch as the being of one thing depends on another, and then we have the third sense; or (2) according to active or passive power, inasmuch as one thing receives something from another or confers it upon the other, and then we have the second sense; or (1) according as the quantity of one thing can be measured by another, and then we have the first sense.
1005. But the quality as such of a thing pertains only to the subject in which it exists, and therefore from the viewpoint of quality one thing bears upon another only inasmuch as quality has the character of an active or passive power, which is a principle of action or of being acted upon. Or it is related by reason of quantity or of something pertaining to quantity; as one thing is said to be whiter than another, or as that which has the same quality as another is said to be like it.
But the other classes of things are a (+) result of relation rather than a (-) cause of it. For the category when consists in a relation to time; and the category where in a relation to place. And posture implies an arrangement of parts; and having (attire), the relation of the thing having to the things had.
1006. The first things (493).
Then he proceeds to deal with the three senses of relation which have been enumerated. First, he considers the first sense. Second (1023), he treats the second sense (“Active and passive”). Third (1026), he attends to the third sense (“Therefore, things”).
In regard to the first he does two things. First, he describes the relations which are based simply on number; and second (1022), he treats those which are based simply on unity (“Further, equal”).
He says, first, that the first way in which things are relative, which is numerical, is divided inasmuch as the relation is based on (a) the ratio of one number to another or (b) on that of a number to unity. And in either case it may be taken in two ways, for the number which is referred to another number or to unity in the ratio on which the relation is based is either definite or indefinite. This is his meaning in saying that the first things which are said to be relative numerically are said to be such “without qualification,” i.e., in general or indefinitely, “or else definitely.” And in both ways “to them,” namely, to numbers, “or to unity,” i.e., to the unit.
1007. Now it should be borne in mind that every measure which is found in continuous quantities is derived in some way from number. Hence relations which are based on continuous quantity are also attributed to number.
1008. It should also be borne in mind that numerical ratios are divided first into two classes, that of equality and that of inequality. And there are two kinds of inequality: the larger and smaller, and more and less.
And the larger is divided into five kinds.
1009. For a number is larger whenever it is multiple with respect to a smaller number, i.e., when it includes it many times, as six includes two three times. And if it includes it twice, it is called double; as two in relation to one, or four to two. And if it includes it three times, it is called triple; and if four times, quadruple; and so on.
1010. But sometimes a larger number includes a whole smaller number once and some part of it besides; and then it is said to be superparticular. If it includes a whole smaller number and a half of it besides, it is called sesquialteral, as three to two; and if a third part besides, it is called sesquitertian, as four to three; and if a fourth part besides, it is called sesquiquartan, as five to four; and so on.
1011. Sometimes a larger number includes a whole smaller number once and not merely one part but many parts besides, and then it is called superpartient. And if it includes two parts, it is called superbipartient, as five to three. Again, if it includes three parts, then it is called supertripartient, as seven to four; and if it includes four parts, it is superquadripartient, and then it is related as nine to five; and so on.
1012. Sometimes a larger number includes a whole smaller number many times and some part of it besides, and then it is called multiple superparticular. If it includes it two and a half times, it is called double sesquialteral, as five to two. If it includes it three and a half times, it is called triple sesquialteral, as seven to two. And if it includes it four and a half times, it is called quadruple sesquialteral, as nine to two. And the species of this kind of ratio can also be considered in the case of the superparticular, inasmuch as we speak of the double sesquitertian ratio when a greater number includes a smaller number two and a third times, as seven to three; or of the double sesquiquartan, as nine to four; and so on.
1013. Sometimes too a larger number includes a whole smaller number many times and many parts of it besides, and then it is called multiple superpartient. And similarly a ratio can be divided from the viewpoint of the species of multiplicity, and from that of the species of the superpartient, provided that we may speak of a double superbipartient, when a greater number includes a whole smaller number twice and two parts of it, as eight to three; or even of triple superbipartient, as eleven to three; or even of double supertripartient, as eleven to four. For it includes a whole number twice and three parts of it besides.
1014. And there are just as many species of inequality in the case of a smaller number. For a smaller number is called submultiple, subpartient, submultiple superparticular, submultiple superpartient, and so on.
1015. But it must be noted that the first species of ratio, namely, multiplicity, consists in the relation of one number to the unit. For any species of it is found first in the relation of some number to the unit. Double, for example, is found first in the relation of two to the unit. And similarly a triple ratio is found in the relation of three to the unit; and so on in other cases. But the first terms in which any ratio is found give species to the ratio itself. Hence in whatever other terms it is subsequently found, it is found in them according to the ratio of the first terms. For example, the double ratio is found first between two and the unit. It is from this, then, that the ratio receives its meaning and name; for a double ratio means the ratio of two to the unit. And it is for this reason too that we use the term in other cases; for even though one number is said to be double another, this happens only inasmuch as a smaller number takes on the role of the unit and a larger number the role of two; for six is related to three in a double ratio, inasmuch as six is to three as two is to one. And it is similar in the case of a triple ratio, and in all other species of multiplicity. Hence he says that the relation of double is a result of the fact that a definite number, i.e., two, “is referred to unity,” i.e., to the unit.
1016. But the term multiple implies the relation of a number to the unit, not of any definite number but of number in general. For if a definite number were taken, as two or three, there would be one species of multiplicity, as double or triple. And just as the double is related to two and the triple to three, which are definite numbers, so too the multiple is related to multiplicity, because it signifies an indefinite number.
1017. Other ratios, however, cannot be reduced to the relation of a number to the unit: either a superparticular ratio, or a superpartient, or a multiple superparticular, or a multiple superpartient. For all of these species of ratios are based on the fact that a larger number includes a smaller number once, or some part of it, and one or several parts of it besides. But the unit cannot have a part, and therefore none of these ratios can be based on the relation of a number to the unit but on the relation of one number to another. Thus the double ratio is either that of a definite number, or that of an indefinite number.
1018. And if it is that of a definite number, then “it is what is one and a half times as great,” i.e., sesquialteral, or “that which it exceeds,” i.e., supersesquialteral. For a sesquialteral ratio consists first in these terms: three and two; and in the ratio of these it is found in all other cases. Hence what is called one and a half times as great, or sesquialteral, implies the relation of one definite number to another, namely, of three to two.
1019. But the relation which is called superparticular is relative to the subparticular, not according to any definite number, as the multiple is relative also to the unit, but according to an indefinite number. For the first species of inequality given above (1008) are taken according to indefinite numbers, for example, the multiple, superparticular, superpartient, and so on. But the species of these are taken according to definite numbers, as double, triple, sesquialteral, sesquiquartan, and so on.
1020. Now it happens that some continuous quantities have a ratio to each other which does not involve any number, either definite or indefinite. For there is some ratio between all continuous quantities, although it is not a numerical ratio. For there is one common measure of any two numbers, namely, the unit, which, when taken many times, yields a number. But no common measure of all continuous quantities can be found, since there are certain incommensurable continuous quantities, as the diameter of a square is incommensurable with one of its sides. The reason is that there is no ratio between it and one of its sides like the ratio of one number to another or of a number to the unit.
1021. Therefore, when it is said in the case of quantities that this quantity is greater than that one, or is related to that one as what includes is related to what is included in it, not only is this ratio not considered according to any definite species of number, but it is not even considered according to number at all, because every number is commensurable with another. For all numbers have one common measure, which is the unit. But what includes and what is included in it are not spoken of according to any numerical measure; for it is what is so much and something more that is said to have the relation of what includes to what is included in it. And this is indefinite, whether it be commensurable or incommensurable; for whatever quantity may be taken, it is either equal or unequal. If it is not equal, then it follows that it is unequal and includes something else, even though it is not commensurable. Hence it is clear that all of the above-mentioned things are said to be relative according to number and to the properties of numbers, which are commensuration, ratio, and the like.
1022. Further, equal (494).
He now treats those relative terms which have a reference to unity or oneness and are not based on the relation of one number to another or to the unit. He says that equal, like and same are said to be relative in a different way than the foregoing. For these are called such in reference to unity. For those things are the same whose substance is one; and those are alike whose quality is one; and those are equal whose quantity is one. Now since unity is the principle and measure of number, it is also clear that the former terms are said to be relative “numerically,” i.e., in reference to something belonging to the class of number. But these last terms are not said to be relative in the same way as the first. For the first relations seen are those of number to number, or of a number to the unit; but this relation has to do with unity in an absolute sense.
1023. Active and passive (495).
(2) Here he proceeds to treat the second type of relations, which pertains to active and passive things. He says that relative beings of this kind are relative in two ways: in one way according to active and passive potency; and in a second way according to the actualizations of these potencies, which are action and passivity; for example, what can heat is said to be relative to what can be heated in virtue of active and passive potency. For it is what is capable of heating that can heat, and it is what is capable of being heated that can become hot. Again, what is heating in relation to what is heated, and what is cutting in relation to what is being cut, are said to be relative according to the operations of the aforesaid potencies.
1024. Now this type of relation differs from those previously given; for those which are numerical are operations only figuratively, for example, to multiply, to divide, and so forth, as has also been stated elsewhere, namely, in Book II of the Physics, where he shows that the objects of mathematics abstract from motion, and therefore they cannot have operations of the kind that have to do with motion.
1025. It should also be noted that among relative terms based on active and passive potency we find diversity from the viewpoint of time; for some of these terms are predicated relatively with regard to past time, as what has made something to what has been made; for instance, a father in relation to his son, because the former has begot and the latter has been begotten; and these differ as what has acted and what has been acted upon. And some are used with respect to future time, as when what will make is related to what will be made. And those relations which are based on privation of potency, as the impossible and the invisible, are reduced to this class of relations. For something is said to be impossible for this person or for that one; and the invisible is spoken of in the same way.
1026. Therefore, things (496).
(3) Next he proceeds to deal with the third type of relations. He says that this third type differs from the foregoing in this way, that each of the foregoing things is said to be relative because each is referred to something else, not because something else is referred to it. For double is related to half, and vice versa; and in a similar way a father is related to his son, and vice versa. But something is said to be relative in this third way because something is referred to it. It is clear, for example, that the sensible and the knowable or intelligible are said to be relative because other things are related to them; for a thing is said to be knowable because knowledge is had of it. And similarly something is said to be sensible because it can be sensed.
1027. Hence they are not said to be relative because of something which pertains to them, such as quality, quantity, action, or undergoing, as was the case in the foregoing relations, but only because of the action of other things, although these are not terminated in them. For if seeing were the action of the one seeing as extending to the thing seen, as heating extends to the thing which can be heated, then just as what can be heated is related to the one heating, so would what is visible be related to the one seeing. But to see and to understand and actions of this kind, as is stated in Book IX (1788) of this work, remain in the things acting and do not pass over into those which are acted upon. Hence what is visible or what is knowable is not acted upon by being known or seen. And on this account these are not referred to other things but others to them. The same is true in all other cases in which something is said to be relative because something else is related to it, as right and left in the case of a pillar. For since right and left designate starting points of motion in living things, they cannot be attributed to a pillar or to any nonliving thing except insofar as living things are related to a pillar in some way. It is in this sense that one speaks of a right-hand pillar because a man stands to the left of it. The same holds true of an image in relation to the original; and of a denarius, by means of which one fixes the price of a sale. And in all these cases the whole basis of relation between two extremes depends on something else. Hence all things of this kind are related in somewhat the same way as what is measurable and its measure. For everything is measured by the thing on which it depends.
1028. Now it must be borne in mind that, even though verbally knowledge would seem to be relative to the knower and to the object of knowledge (for we speak both of the knowledge of the knower and of the knowledge of the thing known), and thought to the thinker and to what is thought, nevertheless a thought as predicated relatively is not relative to the one whose thought it is as its subject, for it would follow that the same relative term would then be expressed twice. For it is evident that a thought is relative to what is thought about as to its object. Again, if it were relative to the thinker, it would then be called relative twice; and since the very existence of what is relative is to be relative in some way to something else, it would follow that the same thing would have two acts of existence. Similarly in the case of sight it is clear that sight is not relative to the seer but to its object, which is color, “or something of this sort.” He says this because of the things which are seen at night but not by means of their proper color, as is stated in The Soul, Book II.
1029. And although it is correct to say that sight is of him who sees, sight is not related to the seer formally as sight but as an accident or power of the seer. For a relation has to do with something external, but a subject does not, except insofar as it is an accident. It is clear, then, that these are the ways in which some things are said to be relative directly.
1030. And other things (497).
He now gives three ways in which some things are said to be relative not directly but indirectly.
The first of these is that in which things are said to be relative because their genera are relative as medicine is said to be relative because science is relative. For medicine is called the science of health and sickness. And science is relative in this way because it is an accident.
1031. The second way is that in which certain abstract terms are said to be relative because the concrete things to which these abstract terms apply are relative to something else. For example, equality and likeness are said to be relative because the like and the equal are relative. But equality and likeness are not considered relative as words.
1032. The third way is that in which a subject is said to be relative because of an accident. For example, a man or some white thing is said to be relative because each happens to be double; and in this way a head is said to be relative because it is a part.

LESSON 18
The Senses of Perfect
ARISTOTLE'S TEXT Chapter 16: 1021b 12-1022a 3
499. That thing is said to be perfect (or complete) outside of which it is impossible to find even a single part; for example, the perfect time of each thing is that outside of which it is impossible to find any time which is a part of it. And those things are perfect whose ability (virtus) and goodness admit of no further degree in their class; for example, we speak of a perfect physician and a perfect flute player when they lack nothing pertaining to the form of their particular ability. And thus in transferring this term to bad things, we speak of a perfect slanderer and a perfect thief, since we also call them good, as a good slanderer and a good thief. For any ability is a perfection, since each thing is perfect and every substance is perfect when, in the line of its particular ability, it lacks no part of its natural measure.
500. Further, those things are said to be perfect which have a goal or end worth seeking. For things are perfect which have attained their goal. Hence, since a goal is something final, we also say, in transferring the term perfect to bad things, that a thing has been perfectly spoiled and perfectly corrupted when nothing pertaining to its corruption and evil is missing but it is at its last point. And for this reason death is described metaphorically as an end; for both of these are final things. But an end is a final purpose.
501. Things which are said to be perfect in themselves, then, are said to be such in all of these senses: some because they lack no part of their goodness and admit of no further degree and have no part outside; others in general inasmuch as they admit of no further degree in any class and have no part outside.
502. And other things are now termed perfect in reference to these, either because they make something such, or have something such, or know something such, or because they are somehow referred to things which are said to be perfect in the primary senses.
COMMENTARY
Perfect
1033. Having treated the various senses of the terms which signify the causes, the subject and the parts of the subject of this science, here the Philosopher begins to treat the various senses of the terms which designate attributes having the character of properties. This is divided into two parts. In the first he gives the various senses of the terms which refer to the perfection or completeness of being. in the second (1128) he treats those which refer to a lack of being (“False means”).
In regard to the first he does two things. First, he gives the different senses of the terms which designate attributes pertaining to the perfection of being; and second (1085), he treats those which designate the wholeness of being. For the terms perfect and whole have the same or nearly the same meaning, as is said in the Physics, Book III. He considers the second part of this division where he says, “To come from something.”
In regard to the first part he does two things. First, he treats the various senses of the term perfect. Second (1044), he treats the various senses of the terms which signify certain conditions of that which is perfect (“The term limit”).
In regard to the first he does two things. First, he considers the senses in which things are said to be perfect in themselves; and second (1043), he treats those in which things are said to be perfect by reason of something else (“And other things”).
In regard to the first he does two things. First, he gives three senses in which a thing is said to be perfect in itself. Second (1040), he shows how, according to these senses, a thing is said to be perfect in different ways (“Things which are said”).
1034. (1) He accordingly says, first, that in one sense that thing is said to be perfect outside of which it is impossible to find any of its parts. For example, a man is said to be perfect when no part of him is missing; and a period of time is said to be perfect when none of its parts can be found outside of it. For example, a day is said to be perfect or complete when no part of it is missing.
1035. (2) A thing is said to be perfect in another sense with reference to some ability. Thus a thing is said to be perfect which admits of “ no further degree,” i.e., excess or superabundance, from the viewpoint of good performance in some particular line, and is not deficient in any respect. For we say that that thing is in a good state which has neither more nor less than it ought to have, as is said in Book II of the Ethics. Thus a man is said to be a perfect physician or a perfect flute player when he lacks nothing pertaining to the particular ability by reason of which he is said to be a good physician or a good flute player. For the ability which each thing has is what makes its possessor good and renders his work good.
1036. And it is in this sense that we also transfer the term perfect to bad things. For we speak of a perfect “slanderer,” or scandal monger, and a perfect thief, when they lack none of the qualities proper to them as such. Nor is it surprising if we use the term perfect of those things which rather designate a defect, because even when things are bad we predicate the term good of them in an analogous sense. For we speak of a good thief and a good scandal monger because in their operations, even though they are evil, they are disposed as good men are with regard to good operations.
1037. The reason why a thing is said to be perfect in the line of its particular ability is that an ability is a perfection of a thing. For each thing is perfect when no part of the natural magnitude which belongs to it according to the form of its proper ability is missing. Moreover, just as each natural being has a definite measure of natural magnitude in continuous quantity, as is stated in Book II of The Soul, So too each thing has a definite amount of its own natural ability. For example, a horse has by nature a definite dimensive quantity, within certain limits; for there is both a maximum quantity and minimum quantity beyond which no horse can go in size. And in a similar way the quantity of active power in a horse has certain limits in both directions. For there is some maximum power of a horse which is not in fact surpassed in any horse; and similarly there is some minimum which never fails to be attained.
1038. Therefore, just as the first sense of the term perfect was based on the fact that a thing lacks no part of the dimensive quantity which itis naturally determined to have, in a similar way this second sense of the term is based on the fact that a thing lacks no part of the quantity of power which it is naturally determined to have. And each of these senses of the term has to do with internal perfection.
1039. Further, those things (500).
(3) Here he gives the third sense in which the term perfect is used, and it pertains to external perfection. He says that in a third way those things are said to be perfect “which have a goal,” i.e., which have already attained their end, but only if that end is “ worth seeking,” or good. A man, for instance, is called perfect when he has already attained happiness. But someone who has attained some goal that is evil is said to be deficient rather than perfect, because evil is a privation of the perfection which a thing ought to have. Thus it is evident that, when evil men accomplish their will, they are not happier but sadder. And since every goal or end is something final, for this reason we transfer the term perfect somewhat figuratively to those things which have reached some final state, even though it be evil. For example, a thing is said to be perfectly spoiled or corrupted when nothing pertaining to its ruin or corruption is missing. And by this metaphor death is called an end, because it is something final. However, an end is not only something final but is also that for the sake of which a thing comes to be. This does not apply to death or corruption.
1040. Here he shows how things are perfect in different ways according to the foregoing senses of perfection. (1) He says that some things are said to be perfect in themselves; and this occurs in two ways. (a) For some things are altogether perfect because they lack absolutely nothing at all; they neither have any “further degree,” i.e., excess, because there is nothing which surpasses them in goodness; nor do they receive any good from outside, because they have no need of any external goodness. This is the condition of the first principle, God, in whom the most perfect goodness is found, and to whom none of all the perfections found in each class of things are lacking.
1041. (b) Some things are said to be perfect in some particular line because “they do not admit of any further degree,” or excess, “in their class,” as though they lacked anything proper to that class. Nor is anything that belongs to the perfection of that class external to them, as though they lacked it; just as a man is said to be perfect when he has already attained happiness.
1042. And not only is this distinction made with reference to the second sense of perfection given above, but it can also be made with reference to the first sense of the term, as is mentioned at the beginning of The Heavens. For any individual body is a perfect quantity in its class, because it has three dimensions, which are all there are. But the world is said to be universally perfect because there is absolutely nothing outside of it.
1043. And other things (502).
(2) He now gives the sense in which some things are said to be perfect by reason of their relation to something else. He says that other things are said to be perfect “in reference to these,” i.e., in reference to things which are perfect in themselves, (a) either because they make something perfect in one of the preceding ways, as medicine is perfect because it causes perfect health; or (b) because they have some perfection, as a man is said to be perfect who has perfect knowledge; or (c) because they represent such a perfect thing, as things which bear a likeness to those that are perfect (as, for example, an image which represents a man perfectly is said to be perfect); or in any other way in which they are referred to things that are said to be perfect in themselves in the primary senses.

LESSON 19
The Senses of Limit, of "According to Which," of "In Itself," and of Disposition
ARISTOTLE'S TEXT Chapters 17 & 18: 1022a 4-1022a 36
503. The term limit (boundary or terminus) means the extremity of anything, i.e., that beyond which nothing of that being can be found, and that within which everything belonging to it is contained.
504. And limit means the form, whatever it may be, of a continuous quantity or of something having continuous quantity; and it also means the goal or end of each thing. And such too is that toward which motion and action proceed, and not that from which they proceed. And sometimes it is both, not only that from which, but also that to which. And it means the reason for which something is done; and also the substance or essence of each. For this is the limit or terminus of knowledge; and if of knowledge, also of the thing.
505. Hence it is clear that the term limit has as many meanings as the term principle has, and even more. For a principle is a limit, but not every limit is a principle.
Chapter 18
506. The phrase according to which (secundum quod) has several meanings. In one sense it means the species or substance of each thing; for example, that according to which a thing is good is goodness itself. And in another sense it means the first subject in 'Whicl~ an attribute is naturally disposed to come into being, as color in. surface. Therefore, in its primary sense, "that according to which" is the form; and in its secondary sense it is the matter of each thing and the first subject of each. And in general that according to which is used in the same way as a reason. For we speak of that according to which he comes, or the reason of his coming; and that according to which he has reasoned incorrectly or simply reasoned, or the reason why he has reasoned or reasoned incorrectly. Further, that according to which 1 is used in reference to place, as according [i.e., next] to which he stands, or according to [i.e., along] which he walks; for in general these signify position and place.
507. Hence the phrase in itself (secundum se) must be used in many senses. For in one sense it means the quiddity of each thing, as Callias and the quiddity of Callias. And in another sense it means everything that is found in the quiddity of a thing. For example, Callias is an animal in himself, because animal belongs to his definition; for Callias is an animal. Again, it is used of a thing when something has been manifested in it as its first subject or in some part of it; for example, a surface is white in itself, and a man is alive in himself. For the soul is a part of man in which life is first present. Again, it means a thing which has no other cause. For there are many causes of man, namely, animal and two-footed, yet man is man in himself. Further, it means any attributes that belong to a thing alone and inasmuch as they belong to it alone, because whatever is separate is in itself.
COMMENTARY
Term/limit
1044. Here Aristotle proceeds to examine the terms which signify the conditions necessary for perfection. Now what is perfect or complete, as is clear from the above, is what is determinate and absolute, independent of anything else, and not deprived of anything but having whatever befits it in its own line. Therefore, first, he deals with the term limit (boundary or terminus); second (1050), with the phrase in itself (“The phrase according to which”); and third (1062), with the term having (“Having means”).
In regard to the first he does three things. First, he gives the meaning of limit. He says that limit means the last part of anything, such that no part of what is first limited lies outside this limit; and all things which belong to it are contained within it. He says “first” because the last part of a first thing may be the starting point of a second thing; for example, the now of time, which is the last point of the past, is the beginning of the future.
1045. And limit means the form (504).
Second, he gives four senses in which the term limit is used:
The first of these applies to any kind of continuous quantity insofar as the terminus of a continuous quantity, or of a thing having continuous quantity, is called a limit; for example, a point is called the limit of a line, and a surface the limit of a body, or also of a stone, which has quantity.
1046. The second sense of limit is similar to the first inasmuch as one extreme of a motion or activity is called a limit, i.e., that toward which there is motion, and not that from which there is motion, as the limit of generation is being and not non-being. Sometimes, however, both extremes of motion are called limits in a broad sense, i.e., both that from which as well as that to which, inasmuch as we say that every motion is between two limits or extremes.
1047. In a third sense limit means that for the sake of which something comes to be, for this is the terminus of an intention, just as limit in the second sense meant the terminus of a motion or an operation.
1048. In a fourth sense limit means the substance of a thing, i.e., the essence of a thing or the definition signifying what a thing is. For this is the limit or terminus of knowledge, because knowledge of a thing begins with certain external signs from which we come to know a thing’s definition, and when we have arrived at it we have complete knowledge of the thing. Or the definition is called the limit or terminus of knowledge because under it are contained the notes by which the thing is known. And if one difference is changed, added, or subtracted, the definition will not remain the same. Now if it [i.e., the definition] is the limit of knowledge, it must also be the limit of the thing, because knowledge is had through the assimilation of the knower to the thing known.
1049. Hence it is clear (505).
Here he concludes by comparing a limit with a principle, saying that limit has as many meanings as principle has, and even more, because every principle is a limit but not every limit is a principle. For that toward which there is motion is a limit, but it is not in any way a principle, whereas that from which there is motion is both a principle and a limit, as is clear from what was said above (1046).
1050. The phrase “according to which” (506).
Here he deals with the phrase in itself; and in regard to this he does three things. First, he lays down the meaning of the phrase according to which, which is more common than the phrase in itself. Second (1054), he draws his conclusion as to the ways in which the phrase in itself is used (“Hence the phrase”). Third (1058), he establishes the meaning of the term disposition, because each of the senses in which we use the phrases mentioned above somehow signifies disposition. In regard to the first, he gives four senses in which the phrase according to which is used:
The first has to do with the “ species,” i.e., the form, or “the substance of each thing,” or its essence, inasmuch as this is that according to which something is said to be; for example, according to the Platonists “the good itself,” i.e., the Idea of the Good, is that according to which something is said to be good.
1051. This phrase has a second meaning insofar as the subject in which some attribute is naturally disposed to first come into being is termed “that according to which,” as color first comes into being in surface; and therefore it is said that a body is colored according to its surface. Now this sense differs from the preceding one, because the preceding sense pertains to form, but this last sense pertains to matter.
1052. There is a third sense in which this phrase is used, inasmuch as any cause or reason in general is said to be “that according to which.” Hence the phrase “according to which” is used in the same number of senses as the term reason. For it is the same thing to ask, “According to what does he come?” and “For what reason does he come? “ And in like manner it is the same to ask, “According to what has he reasoned incorrectly or simply reasoned, and, for what reason has he reasoned?”
1053. This phrase according to which (secundum quid) is used in a fourth sense inasmuch as it signifies position and place; as in the statement, “according to which he stands,” i.e., next to which, and, “according to which he walks,” i.e., along which he walks; and both of these signify place and position. This appears more clearly in the Greek idiom.
1054. Hence the phrase (507).
From what has been said above he draws four senses in which the phrase in itself or of itself is used:
The first of these is found when the definition, which signifies the quiddity of each thing, is said to belong to each in itself, as Callias “and the quiddity of Callias,” i.e., the essence of the thing, are such that one belongs to the other “in itself.” And not only the whole definition is predicated of the thing defined in itself, but so too in a way everything which belongs to the definition, which expresses the quiddity, is predicated of the thing defined in itself. For example, Callias is an animal in himself. For animal belongs in the definition of Callias, because Callias is an individual animal, and this would be given in his definition if individual things could have a definition. And these two senses are included under one, because both the definition and a part of the definition are predicated of each thing in itself for the same reason. For this is the first type of essential predication given in the Posterior Analytics; and it corresponds to the first sense given above (1050) in which we use the phrase according to which.
1055. This phrase is used in a second sense when something is shown to be in something else as in a first subject, when it belongs to it of itself. This can happen in two ways: (a) for either the first subject of an accident is the whole subject itself of which the accident is predicated (as a surface is said to be colored or white in itself; for the first subject of color is surface, and therefore a body is said to be colored by reason of its surface); or (b) also the subject of the accident is some part of the subject, just as a man is said to be alive in himself, because part of him, namely, the soul, is the first subject of life. This is the second type of essential predication given in the Posterior Analytics, namely, that in which the subject is given in the definition of the predicate. For the first and proper subject is given in the definition of a proper accident.
1056. This phrase is used in a third sense when something having no cause is spoken of as in itself; as all immediate propositions, i.e., those which are not proved by a middle term. For in a priori demonstrations the middle term is the cause of the predicate’s belonging to the subject. Hence, although man has many causes, for example, animal and two-footed, which are his formal cause, still nothing is the cause of the proposition “Man is man,” since it is an immediate one; and for this reason man is man in himself.
And to this sense is reduced the fourth type of essential predication given in the Posterior Analytics, the case in which an effect is predicated of a cause; as when it is said that the slain man perished by slaying, or that the thing cooled was made cold or chilled by cooling.
1057. This phrase is used in a fourth sense inasmuch as those things are said to belong to something in themselves which belong to it alone and precisely as belonging to it alone. He says this in order to differentiate this sense of in itself from the preceding senses, in which it was not said that a thing belongs to something in itself because it belongs to it alone; although in that sense too something would belong to it alone, as the definition to the thing defined. But here something is said to be in itself by reason of its exclusiveness. For in itself signifies something separate, as a man is said to be by himself when he is alone.
And to this sense is reduced the third sense given in the Posterior Analytics, and the fourth sense of the phrase according to which, which implies position.

LESSON 20
The Meanings of Disposition, of Having, of Affection, of Privation, and of "To Have"
ARISTOTLE'S TEXT Chapters 19-23: 1022b 1-1023a 25
508. Disposition means the order of what has parts, either as to place or as to potentiality or as to species. For there must be a certain position, as the term disposition itself makes clear.
Chapter 20
509. Having (possession or habit) means in one sense a certain activity of the haver and of the thing had, as a sort of action or motion. For when one thing makes and another is made, the making is intermediate. And likewise between one having clothing and the clothing had, the having is intermediate. It is accordingly clear that it is not reasonable to have a having; for if it were possible to have the having of what is had, this would go on to infinity. In another sense having means a certain disposition whereby the thing disposed is well or badly disposed, either in relation to itself or to something else; for example, health is a sort of having and is such a disposition. Again, the term having is used if there is a part of such a disposition. And for this reason any virtue pertaining to the powers of the soul is a sort of having.
Chapter 21
510. Affection (passio) means in one sense (modification), the quality according to which alteration occurs, as white and black, sweet and bitter, heavy and light, and all other such attributes. And in another sense (undergoing), it means the actualizations and alterations of these; and of these, particularly harmful operations and motions; and most especially those which are painful and injurious (suffering). Again, great rejoicing and grieving are called affections (passions).
Chapter 22
511. The term privation is used in one sense when a thing does not have one of those attributes which it is suitable for some things to have, even though that particular thing would not naturally have it. In this sense a plant is said to be deprived of eyes. And it is used in another sense when a thing is naturally disposed to have something, either in itself or according to its class, and does not have it. A man and a mole, for example, are deprived of sight but in different ways: the latter according to its class and the former in itself. Again, we speak of privation which a thing is by nature such as to have a certain perfection and does not have it even when it is naturally disposed to have it. For blindness is a privation, although a man is not blind at every age but only if he does not have sight at the age when he is naturally disposed to have it. And similarly we use the term privation when a thing does not have some attribute which it is naturally disposed to have, in reference to where, and to what and to the object in relation to which, and in the manner in which it may have it by nature if it does not have it. Again, the removal of anything by force is called a privation.
512. And in all instances in which negations are expressed by the privative particle & [i.e., un- or in-], privations are expressed. For a thing is said to be unequal because it does not have the equality which it is naturally fitted to have. And a thing is said to be invisible either because it has no color at all or because its color is deficient; and a thing is said to be footless either because it lacks feet altogether or because its feet are imperfect. Again, we use the term privation of a thing when it has something to a very small degree, for example, "unignited," and this means to have it in a deficient way. And privation also designates what is not had easily or well; for example, a thing is uncuttable not only because it cannot be cut but because it cannot be cut easily or well. And we use the term privation of what is not had in any way. For it is not only a one-eyed man that is said to be blind, but one who lacks sight in both eyes. And for this reason not every man is good or bad, just or unjust, but there is an intermediate state.
Chapter 23
513. To have (to possess or to hold) has many meanings. In one sense it means to treat something according to one's own nature or to one's own impulse; and for this reason a fever is said to possess a man, and tyrants are said to possess cities, and people who are clothed are said to possess clothing. And in another sense a thing is said to have something when this is present in the subject which receives it; thus bronze has the form of a statue, and a body, disease. And whatever contains something else is said to have or to hold it; for that which is contained is said to be held by the container; for example, we say that a bottle holds a liquid and a city men and a ship sailors. It is in this way too that a whole has parts. Again, whatever prevents a thing from moving or from acting according to its own impulse is said to hold it, as pillars hold the weight imposed on them. It is in this sense that the poets make Atlas hold the heavens, as if otherwise it would fall on the earth, as certain of the physicists also say. And it is in this sense that that which holds something together is said to hold what it holds together, because otherwise it would be separated, each according to its own impulse. And to be in something is expressed in a similar way and corresponds to the meanings of to have.
COMMENTARY
Disposition
1058. Because the phrase according to which signifies in one sense position, the Philosopher therefore proceeds to examine next (1058) the term disposition. He gives the common meaning of this term, saying that a disposition is nothing else than the order of parts in a thing which has parts. He also gives the senses in which the term disposition is used; and there are three of these:
The first designates the order of parts in place, and in this sense disposition or posture is a special category.
1059. Disposition is used in a second sense inasmuch as the order of parts is considered in reference to potency or active power, and then disposition is placed in the first species of quality. For a thing is said to be disposed in this sense, for example, according to health or sickness, by reason of the fact that its parts have an order in its active or passive power.
1060. Disposition is used in a third sense according as the order of parts is considered in reference to the form and figure of the whole; and then disposition or position is held to be a difference in the genus of quantity. For it is said that one kind of quantity has position, as line, surface, body and place, but that another has not, as number and time.
1061. He also points out that the term disposition signifies order; for it signifies position, as the derivation itself of the term makes clear, and order is involved in the notion of position.
1062. “having” means (509).
He now proceeds to examine the term having. First, he gives the different senses of the term having. Second (1065), he gives the different senses of certain other terms which are closely connected with this one. He accordingly gives, first, the two senses in which the term having is used:
First, it designates something intermediate between the haver and the thing had. Now even though having is not an action, nonetheless it signifies something after the manner of an action. Therefore having is understood to be something intermediate between the haver and the thing had and to be a sort of action; just as heating is understood to be something intermediate between the thing being heated and the heater, whether what is intermediate be taken as an action, as when heating is taken in an active sense, or as a motion, as when heating is taken in a passive sense. For when one thing makes and another is made, the making stands between them. In Greek the term poi,hsij is used, and this signifies making. Moreover, if one goes from the agent to the patient, the intermediate is making in an active sense, and this is the action of the maker. But if one goes from the thing made to the maker, then the intermediate is making in a passive sense, and this is the motion of the thing being made. And between a man having clothing and the clothing had, the having is also an intermediate; because, if we consider it by going from the man to his clothing, it will be like an action, as is expressed under the form “to have.” But if we consider it in the opposite way, it will be like the undergoing of a motion, as is expressed under the form “to be had.”
1063. Now although having is understood to be intermediate between a man and his clothing inasmuch as he has it, nonetheless it is evident that there cannot be another intermediate between the having and the thing had, as though there were another having midway between the haver and the intermediate having. For if one were to say that it is possible to have the having “of what is had,” i.e., of the thing had, an infinite regress would then result. For the man has “the thing had,” i.e., his clothing, but he does not have the having of the thing had by way of another intermediate having. It is like the case of a maker, who makes the thing made by an intermediate making, but does not make the intermediate making itself by way of some other intermediate making. It is for this reason too ‘that the relations by which a subject is related to something else are not related to the subject by some other intermediate relation and also not to the opposite term; paternity, for example, is not related to a father or to a son by some other intermediate relation. And if some relations are said to be intermediate, they are merely conceptual relations and not real ones. Having in this sense is taken as one of the categories.
1064. In a second sense the term having means the disposition whereby something is well or badly disposed; for example, a thing is well disposed by health and badly disposed by sickness. Now by each of these, health and sickness, a thing is well or badly disposed in two ways: in itself or in relation to something else. Thus a healthy thing is one that is well disposed in itself, and a robust thing is one that is well disposed for doing something. Health is a kind of having, then, because it is a disposition such as has been described. And having (habit) designates not only the disposition of a whole but also that of a part, which is a part of the disposition of the whole. For example, the good dispositions of an animal’s parts are themselves parts of the good disposition of the whole animal. The virtues pertaining to the parts of the soul are also habits; for example, temperance is a habit of the concupiscible part, fortitude a habit of the irascible part, and prudence a habit of the rational part.
1065. “Affection” Here he proceeds to treat the terms which are associated with having. First, he deals with those which are associated as an opposite; and second (1080), he considers something which is related to it as an effect, namely, to have, which derives its name from having.
Now there is something which is opposed to having as the imperfect is opposed to the perfect, and this is affection (being affected). And privation is opposed by direct opposition. Hence, first (1065), he deals with affection; and second (1070), with privation (“The term privation”). He accordingly gives, first, four senses of the term affection.:
In one sense (modification) it means the quality according to which alteration takes place, such as white and black and the like. And this is the third species of quality; for it has been proved in Book VII of the Physics that there can be alteration only in the third species of quality.
1066. Affection is used in another sense (undergoing) according as the actualizations of this kind of quality and alteration, which comes about through them, are called affections. And in this sense affection is one of the categories, for example, being heated and cooled and other motions of this kind.
1067. In a third sense (suffering) affection means, not any kind of alteration at all, but those which are harmful and terminate in some evil, and which are lamentable or sorrowful; for a thing is not said to suffer insofar as it is healed but insofar as it is made ill. Or it also designates anything harmful that befalls anything at alland with good reason. For a patient by the action of some agent which is contrary to it is drawn from its own natural disposition to one similar to that of the agent. Hence, a patient is said more properly to suffer when some part of something fitting to it is being removed and so long as its disposition is being changed into a contrary one, than when the reverse occurs. For then it is said rather to be perfected.
1068. And because things which are not very great are considered as nothing, therefore in a fourth sense (passion) affection means not any kind of harmful alteration whatsoever, but those which are extremely injurious, as great calamities and great sorrows. And because excessive pleasure becomes harmful (for sometimes people have died or become ill as a result of it) and because too great prosperity is turned into something harmful to those who do not know how to make good use of it, therefore another text reads “great rejoicing and grieving are called affections.” And still another text agrees with this, saying, “very great sorrows and prosperities.”
1069. Now it should be noted that because these three—disposition, habit or having, and affection— signify one of the categories only in one of the senses in which they are used, as is evident from what was said above, he therefore did not place them with the other parts of being, i.e., with quantity, quality and relation. For either all or most of the senses in which they were used pertained to the category signified by these terms.
1070. The term “privation” (511).
Here he gives the different senses in which the term privation is used. And since privation includes in its intelligible structure both negation and the fitness of some subject to possess some attribute, he therefore gives, first, the different senses of privation which refer to this fitness or aptitude for some attribute. Second (1074), he treats the various senses of negation (“And in all instances”). In regard to the first he gives four senses of privation:
The first has to do with this natural fitness taken in reference to the attribute of which the subject is deprived and not in reference to the subject itself. For we speak of a privation in this sense when some attribute which is naturally fitted to be had is not had, even though the subject which lacks it is not designed by nature to have it. For example, a plant is said to be deprived of eyes because eyes are naturally designed to be had by something, although not by a plant. But in the case of those attributes which a subject is not naturally fitted to have, the subject cannot be said to be deprived of them, for example, that the eye by its power of vision should penetrate an opaque body.
1071. A second sense of the term privation is noted in reference to a subject’s fitness to have some attribute. For in this sense privation refers only to some attribute which a thing is naturally fitted to have either in itself or according to its class; in itself, for example, as when a blind person is said to be deprived of sight, which he is naturally fitted to have in himself. And a mole is said to be deprived of sight, not because it is naturally fitted to have it, but because the class, animal, to which the mole belongs, is so fitted. For there are many attributes which a thing is not prevented from having by reason of its genus but by reason of its differences; for example, a man is not prevented from having wings by reason of his genus but by reason of his difference.
1072. A third sense of the term privation is noted in reference to circumstances. And in this sense a thing is said to be deprived of something if it does not have it when it is naturally fitted to have it. This is the case, for example, with the privation blindness; for an animal is not said to be blind at every age but only if it does not have sight at an age when it is naturally fitted to have it. Hence a dog is not said to be blind before the ninth day. And what is true of the circumstance when also applies to other circumstances, as “to where,” or place. Thus night means the privation of light in a place where light may naturally exist, but not in caverns, which the sun’s rays cannot penetrate. And it applies “to what part,” as a man is not said to be toothless if he does not have teeth in his hand but only if he does not have them in that part in which they are naturally disposed to exist; and “to the object in relation to which,” as a man is not said to be small or imperfect in stature if he is not large in comparison with a mountain or with any other thing with which he is not naturally comparable in size. Hence a man is not said to be slow in moving if he does not run as fast as a hare or move as fast as the wind; nor is he said to be ignorant if he does not understand as God does.
1073. Privation is used in a fourth sense inasmuch as the removal of anything by violence or force is called a privation. For what is forced is contrary to natural impulse, as has been said above (829); and thus the removal of anything by force has reference to something that a person is naturally fitted to have.
1074. And in all (512).
Then he gives the different senses of privation which involve negation:
For the Greeks use the prefix av -, when compounding words, to designate negations and privations, just as we use the prefix in- or un-; and therefore he says that in every case in which one expresses negations designated by the prefix av -, used in composition at the beginning of a word, privations are designated. For unequal means in one sense what lacks equality, provided that it is naturally such as to have it; and invisible means what lacks color; and footless, what lacks feet.
1075. Negations of this kind are used in a second sense to indicate not what is not had at all but what is had badly or in an ugly way; for example, a thing is said to be colorless because it has a bad or unfitting color; and a thing is said to be footless because it has defective or deformed feet.
1076. In a third sense an attribute is signified privatively or negatively because it is had to a small degree; for example, the term avpu,rhnon i.e., unignited, is used in the Greek text, and it signifies a situation where the smallest amount of fire exists. And in a way this sense is contained under the second, because to have something to a small degree is in a way to have it defectively or unfittingly.
1077. Something is designated as a privation or negation in a fourth sense because it is not done easily or well; for example, something is said to be uncuttable not only because it is not cut but because it is not cut easily or well.
1078. And something is designated as a privation or negation in a fifth sense because it is not had in any way at all. Hence it is not a one-eyed person who is said to be blind but one who lacks sight in both eyes.
1079. From this he draws a corollary, namely, that there is some intermediate between good and evil, just and unjust. For a person does not become evil when he lacks goodness to any degree at all, as the Stoics said (for they held all sins to be equal), but when he deviates widely from virtue and is brought to a contrary habit. Hence it is said in Book II of the Ethics that a man is not to be blamed for deviating a little from virtue.
1080. “To have” (513).
Then he gives four ways in which the term to have (to possess or hold) is used:
First, to have a thing is to treat it according to one’s own nature in the case of natural things, or according to one’s own impulse in the case of voluntary matters. Thus a fever is said to possess a man because he is brought from a normal state to one of fever. And in the same sense tyrants are said to possess cities, because civic business is carried out according to the will and impulse of tyrants. And in this sense too those who are clothed are said to possess or have clothing, because clothing is fitted to the one who wears it so that it takes on his figure. And to have possession of a thing is also reduced to this sense of to have, because anything that a man possesses he uses as he wills.
1081. To have is used in a second way inasmuch as that in which some attribute exists as its proper subject is said to have it. It is in this sense that bronze has the form of a statue, and a body has disease. And to have a science or quantity or any accident or form is included under this sense.
1082. To have is used in a third way (to hold) when a container is said to have or to hold the thing contained, and the thing contained is said to be held by the container. For example, we say that a bottle has or “holds a liquid,” i.e., some fluid, such as water or wine; and a city, men; and a ship, sailors.
It is in this sense too that a whole is said to have parts; for a whole contains a part just as a place contains the thing in place. But a place differs from a whole in this respect that a place may be separated from the thing which occupies it, whereas a whole may not be separated from its parts. Hence, anything that occupies a place is like a separate part, as is said in Book IV of the Physics.
1083. To have is used in a fourth way (to hold up) inasmuch as one thing is said to hold another because it prevents it from operating or being moved according to its own impulse. It is in this sense that pillars are said to hold up the heavy bodies placed upon them, because they prevent these bodies from falling down in accordance with their own inclination. And in this sense too the poets said that Atlas holds up the heavens; for the poets supposed Atlas to be a giant who prevents the heavens from falling on the earth. And certain natural philosophers also say this, holding that the heavens will at some time be corrupted and fall in dissolution upon the earth. This is most evident in the opinions expressed by Empedocles, for he held that the world is destroyed an infinite number of times and comes into being an infinite number of times. And the fables of the poets have some basis in reality; for Atlas, who was a great astronomer, made an accurate study of the motion of the celestial bodies, and from this arose the story that he holds up the heavens.
But this sense of the term to have differs from the first. For according to the first, as was seen, the thing having compels the thing had to follow by reason of its own impulse, and thus is the cause of forced motion. But here the thing having prevents the thing had from being moved by its own natural motion, and thus is the cause of forced rest.
The third sense of having, according to which a container is said to have or hold the thing contained, is reduced to this sense, because the individual parts of the thing contained would be separated from each other by their own peculiar impulse if the container did not prevent this. This is clear, for example, in the case of a bottle containing water, inasmuch as the bottle prevents the parts of the water from being separated.
1084. In closing he says that the phrase to be in a thing is used in the same way as to have, and the ways of being in a thing correspond to those of having a thing. Now the eight ways of being in a thing have been treated in Book IV of the Physics. Two of these are as follows: (1&2) that in which an integral whole is in its parts, and the reverse of this. Two others are: (3&4) the way in which a universal whole is in its parts, and vice versa. (8) And another is that in which a thing in place is in a place, and this corresponds to the third sense of having, according to which a whole has parts, and a place thas the thing which occupies it. (6) But he way in which a thing is said to be in something as in an efficient cause or mover (as the things belonging to a kingdom are in the king) corresponds to the first sense of having given here (1080). (7) And the way in which a thing is in an end or goal is reduced to the fourth sense of having given here (1083), or also to the first, because those things which are related to an end are moved or at rest because of it. [(5) The way health is in a balance of temperature, and any form is in matter or a subject, whether the form be accidental or substantial.]

LESSON 21
The Meanings of "To Come from Something," Part, Whole, and Mutilated
ARISTOTLE'S TEXT Chapters 24-27: 10:23a 26-1024a 28
514. To come from something (esse or fieri ex aliquo) means in one sense to come from something as matter, and this in two ways: either in reference to the first genus or to the ultimate species; for example, all liquefiable things come from water, and a statue comes from bronze. And in another sense it means to come from a thing as a first moving principle; for example, From what did the fight come? From a taunt; because this was the cause of the fight. In another sense it means to come from the composite of matter and form, as parts come from a whole, and a verse from the Iliad, and stones from a house. For the form is an end or goal, and what is in possession of its end is complete. And one thing comes from another in the sense that a species comes from a part of a species, and man from two-footed, and a syllable from an element. For this is different from the way in which a statue comes from bronze, because a composite substance comes from sensible matter, but a species also comes from the matter of a species. These are the senses, then, in which some things are said to come from something. But other things are said to come from something if they come from a part of that thing in any of the aforesaid senses. For example, a child comes from its father and mother, and plants come from the earth, because they come from some part of them. And some things come from others only because they come one after the other in time, as night comes from day, and a storm from a calm. And some of these are so described only because they admit of change into each other, as in the cases just mentioned. And some only because they follow one another in time, as a voyage is made from the equinox because it takes place after the equinox. And feasts come one from another in this way, as the Thargelian from the Dionysian, because it comes after the Dionysian.
Chapter 25
515. Part means in one sense that into which a quantity is divided in any way; for what is subtracted from a quantity is always called a part of it. For example, the number two is said in a sense to be a part of the number three. And in another sense part means only such things as measure a whole. And for this reason the number two is said in a sense to be a part of the number three, and in another, not. Again, those things into which a species is divided irrespective of quantity are also called parts of this species; and it is for this reason that species are said to be parts of a genus. Again, parts mean those things into which a whole is divided or of which a whole is composed, whether the whole is a species or the thing having the species, as bronze is a part of a bronze sphere or of a bronze cube (for this is the matter in which the form inheres). An angle also is a part. And those elements contained in the intelligible expression, which manifests what each thing is, are also parts of a whole. And for this reason the genus is also called a part of the species, although in another respect the species is called a part of the genus.
Chapter 26
516. Whole means that from which none of the things of which it is said to consist by nature are missing; and that which contains the things contained in such a way that they form one thing.
517. But this occurs in two ways: either inasmuch as each is the one in question, or inasmuch as one thing is constituted of them.
518. For a whole is a universal or what is predicated in general as being some one thing as a universal is one, in the sense that it contains many things, because it is predicated of each, and all of them taken singly are that one thing, as man, horse and god, because all are living things.
519. A whole is something continuous and limited when one thing is constituted of many parts which are present in it, particularly when they are present potentially; but if not, even when they are present in activity.
520. And of these same things, those which are wholes by nature are such to a greater degree than those which are wholes by art, as we also say of a thing that is one (424:C 848), inasmuch as wholeness is a kind of unity.
521. Again, since a quantity has a beginning, a middle point and an end, those quantities to which position makes no difference we designate by the term all; but those to which position makes a difference we designate by the term whole; and those to which both descriptions apply we designate by both terms—all and whole. Now these are the things whose nature remains the same in being rearranged but whose shape does not, as wax and a garment; for both all and whole are predicated of them since they verify both. But water and all moist things and number have all applied to them, although water and number are called wholes only in a metaphorical sense. But those things of which the term every is predicated with reference to one, have the term all predicated of them with reference to several, for example, all this number, all these units.
Chapter 27
522. It is not any quantity at all that is said to be mutilated, but it must be a whole and also divisible. For two things are not mutilated when one is taken away from the other, because the mutilated part is never equal to the remainder. And in general no number is mutilated, for its substance must remain. If a goblet is mutilated it must still be a goblet; but a number is not the same when a part is taken away. Again, all things composed of unlike parts are not said to be mutilated. For a number is like something having unlike parts, as two and three. And in general those things to which position makes no difference, such as water and fire, are not mutilated; but they must have position in their substance. And they must be continuous; for a harmony is made up of unlike parts and has position but is not mutilated.
523. Further, neither is every whole mutilated by the privation of every part. For the parts which are removed must not be things which are proper to the substance or things which exist anywhere at all; for example, a goblet is not mutilated if a hole is made in it, but only if an ear or some extremity is removed; and a man is not mutilated if his flesh or spleen is removed, but only if an extremity is removed. And this means not any extremity whatever, but those which, when removed from the whole, cannot regenerate. Hence to have one’s head shaven is not a mutilation.
COMMENTARY
Part
1085. Here he begins to treat the things which pertain to the notion of whole and part. First, he deals with those which pertain to the notion of part; and second (1098), with those which pertain to the notion of whole (“Whole means”).
And because a whole is constituted of parts, he therefore does two things in dealing with the first member of this division. First, he explains the various ways in which a thing is said to come from something; and second (1093), he considers the different senses in which the term part is used (“Part means”).
In regard to the first he does three things. First, he considers the ways in which a thing is said to come from something in the primary and proper sense. Second (1090), he indicates the ways in which one thing comes from another but not in the primary sense (“But other things”). Third (1091), he considers the ways in which one thing comes from another but not in the proper sense (“And some things”). In dealing with the first part he gives four ways in which a thing is said to come from something:
First, a thing is said to come from something as from matter, and this can happen in two ways: (a) In one way, inasmuch as matter is taken to be “the matter of the first genus,” i.e., common matter; as water is the matter of all liquids and liquables, all of which are said to come from water. (b) In another way, “in reference to the ultimate species,” i.e., the lowest species; as the species statue is said to come from bronze.
1086. In a second way a thing is said to come from something as “from a first moving principle,” as a fight comes from a taunt, which is the principle moving the soul of the taunted person to fight. And it is in this way too that a house is said to come from a builder, and health from the medical art.
1087. In a third way one thing is said to come from another as something simple “comes from the composite of matter and form.” This pertains to the process of dissolution; and it is in this way that we say parts come from a whole, “and a verse from the Iliad” (i.e., from the whole treatise of Homer about Troy); for the Iliad is divided into verses as a whole is divided into parts. And it is in the same way that stones are said to come from a house. The reason for this is that the form is the goal or end in the process of generation; for it is what has attained its end that is said to be perfect or complete, as was explained above (500:C 1039). Hence it is evident that that is perfect which has a form. Therefore, when a perfect whole is broken down into its parts, there is motion in a sense from form to matter; and in a similar way when parts are combined, there is an opposite motion from matter to form. Hence the preposition from, which designates a beginning, applies to both processes: both to the process of composition, because it signifies a material principle, and to that of dissolution, because it signifies a formal principle.
1088. In a fourth way a thing is said to come from something as “a species comes from a part of a species.” And part of a species can be taken in two ways: either in reference to the conceptual order or to the real order. (a) It is taken in reference to the conceptual order when we say, for example, that two-footed is a part of man; because while it is part of his definition, it is not a real part, otherwise it would not be predicated of the whole. For it is proper to the whole man to have two feet. (b) And it is taken in reference to the real order when we say, for example, that “a syllable comes from an element,” or letter, as from a part of the species. But here the fourth way in which the term is used differs from the first; for in the first way a thing was said to come from a part of matter, as a statue comes from bronze. For this substance, a statue, is composed of sensible matter as a part of its substance. But this species is composed of part of the species.
1089. For some parts are parts of a species and some are parts of matter. Those which are called parts of a species are those on which the perfection of the species depends and without which it cannot be a species. And it is for this reason that such parts are placed in the definition of the whole, as body and soul are placed in the definition of an animal, and an angle in the definition of a triangle, and a letter in the definition of a syllable. And those parts which are called parts of matter are those on which the species does not depend but are in a sense accidental to the species; for example, it is accidental to a statue that it should come from bronze or from any particular matter at all. And it is also accidental that a circle should be divided into two semi-circles; and that a right angle should have an acute angle as part of it. Parts of this sort, then, are not placed in the definition of the whole species but rather the other way around, as will be shown in Book VII of this work (1542). Hence it is clear that in this way some things are said to come from others in the primary and proper sense.
1090. But some things are said to come from something not in the (~) primary sense but (+)according to a part of that thing in “any of the aforesaid senses.” For example, a child is said to come from its father as an efficient principle, and from its mother as matter; because a certain part of the father causes motion, i.e., the sperm, and a certain part of the mother has the character of matter, i.e., the menstrual fluid. And plants come from the earth, although not from the whole of it but from some part.
1091. And in another way a thing is said to come from something in an improper sense, namely, from the fact that this implies order or succession alone; and in this way one thing is said to come from another in the sense that it comes after it, as “night comes from day,” i.e., after the day, “and a storm from a calm,” i.e., after a calm. And this is said in reference to two things. For in those cases in which one thing is said to come from another, order is sometimes noted in reference to motion and not merely to time; because either they are the two extremes of the same motion, as when it is said that white comes from black, or they are a result of different extremes of the motion, as night and day are a result of different locations of the sun. And the same thing applies to winter and summer. Hence in some cases one thing is said to come from another because one is changed into the other, as is clear in the above examples.
1092. But sometimes order or succession is considered in reference to time alone; for example, it is said that “a voyage is made from the equinox,” i.e., after the equinox. For these two extremes are not extremes of a single motion but pertain to different motions. And similarly it is said that the Thargelian festival [of Apollo and Artemis] comes from the Dionysian because it comes after the Dionysian, these being two feasts which were celebrated among the gentiles, one of which preceded the other in time.
1093. “Part” means (515).
He now gives four senses in which something is said to be a part:
In one sense part means that into which a thing is divided from the viewpoint of quantity; and this can be taken in two ways. (a) For, in one way, no matter how much smaller that quantity may be into which a larger quantity is divided, it is called a part of this quantity. For anything that is taken away from a quantity is always called a part of it; for example, the number two is in a sense a part of the number three. (b) And, in another way, only a smaller quantity which measures a larger one is called a part. In this sense the number two is not a part of the number three but a part of the number four, because two times two equals four.
1094. In a second sense parts mean those things into which something is divided irrespective of quantity; and it is in this sense that species are said to be parts of a genus. For a genus is divided into species, but not as a quantity is divided into quantitative parts. For a whole quantity is not in each one of its parts, but a genus is in each one of its species.
1095. In a third sense parts mean those things into which some whole is divided or of which it is composed, whether the whole is a species or the thing having a species, i.e., the individual. For, as has been pointed out already (1089), there are parts of the species and parts of matter, and these (species and matter) are parts of the individual. Hence bronze is a part of a bronze sphere or of a bronze cube as the matter in which the form is received, and thus bronze is not a part of the form but of the thing having the form. And a cube is a body composed of square surfaces. And an angle is part of a triangle as part of its form, as has been stated above (1099).
1096. In a fourth sense parts mean those things which are placed in the definition of anything, and these are parts of its intelligible structure; for example, animal and two-footed are parts of man.
1097. From this it is clear that a genus is part of a species in this fourth sense, but that a species is part of a genus in a different sense, i.e., in the second sense. For in the second sense a part was taken as a subjective part of a universal whole, whereas in the other three senses it was taken as an integral part. And in the first sense it was taken as a part of quantity; and in the other two senses as a part of substance; yet in such a way that a part in the third sense means a part of a thing, whether it be a part of the species or of the individual. But in the fourth sense it is a part of the intelligible structure.
Whole
1098. “Whole” means (516).
He proceeds to treat the things which pertain to a whole. First, he considers a whole in a general way; and second (1119), he deals with a particular kind of whole, namely a genus.
In regard to the first part he does two things. First, he proceeds to deal with the term whole; and second 1109), with its opposite, mutilated.
In regard to the first he does three things. First, he states the common meaning of whole, which involves two things. (1) The first is that the perfection of a whole is derived from its parts. He indicates this when he says “a whole means that from which none of the things,” i.e., the parts, “of which it is said to consist by nature,” i.e., of which the whole is composed according to its own nature, “are missing.” (2) The second is that the parts become one in the whole. Thus he says that a whole is “that which contains the things contained,” namely, the parts, in such a way that the things contained in the whole are some one thing.
1099. But this occurs. (517).
Second, he notes two ways in which a thing is a whole. He says that a thing is said to be a whole in two ways: (1) either in the sense that each of the things contained by the containing whole is “the one in question,” i.e., the containing whole, which is in the universal whole that is predicated of any one of its own parts; or (2) in the sense that it is one thing composed of parts in such a way that none of the parts are that one thing. This is the notion of an integral whole, which is not predicated of any of its own integral parts.
1100. For a whole (518).
Third, he explains the foregoing senses of whole. First, he explains the first sense. He says that a whole is a universal “or what is predicated in general,” i.e., a common predicate, as being some one thing as a universal is one, in the sense that it is predicated of each individual just as the universal, which contains many parts, is predicated of each of its parts. And all of these are one in a universal whole in such a way that each of them is that one whole; for example, living thing contains man and horse and god, because “all are living things,” i.e., because living thing is predicated of each. By a god he means here a celestial body, such as the sun or the moon, which the ancients said were living bodies and considered to be gods; or he means certain ethereal living beings, which the Platonists called demons, and which were worshipped by the pagans as gods.
1101. A whole is something (519).
Second, he explains the meaning of whole in the sense of an integral whole; and in regard to this he does two things. First, he gives the common meaning of this kind of whole, and particularly of that which is divided into quantitative parts, which is more evident to us. He says that a whole is something “continuous and limited,” i.e., perfect or complete (for what is unlimited does not have the character of a whole but of a part, as is said in Book III of the Physics when one thing is composed of many parts which are present in it. He says this in order to exclude the sense in which one thing comes from another as from a contrary.
1102. Now the parts of which a whole is composed can be present in it in two ways: in one way potentially, and in another actually. Parts are potentially present in a whole which is continuous, and actually present in a whole which is not continuous, as stones are actually present in a heap. But that which is continuous is one to a greater degree, and therefore is a whole to a greater degree, than that which is not continuous. Hence he says that parts must be present in a whole, especially potential parts, as they are in a continuous whole; and if not potentially, then at least “in activity,” or actually. For “activity” means interior action.
1003. Now although a thing is a whole to a greater degree when its parts are present potentially than when they are present actually, nonetheless if we look to the parts, they are parts to a greater degree when they exist actually than when they exist potentially. Hence another text reads, “especially when they are present perfectly and actually; but otherwise, even when they are present potentially.” And it also adds the words given above: “particularly when they are present potentially; but if not, even when they are present in activity.” Hence it seems that the translator found two texts, which he translated, and then made the mistake of combining both so as to make one text. This is clear from another translation, which contains only one of these statements; for it reads as follows: “And a whole is continuous and limited when some one thing, is composed of many intrinsic parts, especially when they are present potentially; but if not, when they are present actually.”
1104. And of these same things (520).
Second, he indicates two differences within this second sense of whole. The first is that some continuous things are such by art and some by nature. Those which are continuous by nature are “such,” i.e., wholes, to a greater degree than those which are such by art. And since we spoke in the same way above (848) about things which are one, saying that things which are continuous by nature are one to a greater degree, as though wholeness were oneness, it is clear from this that anything which is one to a greater degree is a whole to a greater degree.
1105. Again, since a quantity (521).
He gives the second difference. For since it is true that there is an order of parts in quantity, because a quantity has a beginning, a middle point and an end, and the notion of position involves these, the positions of the parts in all these quantities must be continuous. But if we consider the position of the parts, a whole is found to be continuous in three ways. (1) For there are some wholes which are unaffected by a difference of position in their parts. This is evident in the case of water, for it makes no difference how the parts of water are interchanged. The same thing is true of other liquids, as oil and wine and the like. And in these things a whole is signified by the term all and not by the term whole. For we say all the water or all the wine or all the numbers, but not the whole, except metaphorically. This perhaps applies to the Greek idiom, but for us it is a proper way of speaking.
1106. (2) And there are some things to which the position of the parts does make a difference, for example, a man and any animal and a house and the like. For a thing is not a house if its parts are arranged in just any way at all, but only if they have a definite arrangement; and of these we use the term whole and not the term all. And similarly a thing is not a man or an animal if its parts are arranged in just any way at all. For when we speak of only one animal, we say the whole animal and not all the animal.
1107. (3) And there are some things to which both of these apply, because in a sense the position of their parts accounts for their differences; and of these we use both terms— all and whole. And these are the things in which, when the parts are interchanged, the matter remains the same but not the form or shape. This is clear, for example, in the case of wax; for no matter how its parts are interchanged the wax still remains, but it does not have the same shape. The same is true of a garment and of all things which have like parts and take on a different shape. For even though liquids have like parts, they cannot have a shape of their own, because they are not limited by their own boundaries but by those of other things. Hence when their parts are interchanged no change occurs in anything that is proper to them.
1108. The reason for this difference is that the term all is distributive and therefore requires an actual multitude or one in proximate potency to act; and because those things have like parts, they are divided into parts entirely similar to the whole, and in that manner multiplication of the whole takes place. For if every part of water is water, then in each part of water there are many waters, although they are present potentially, just as in one number there are many units actually. But a whole signifies a collection of parts into some one thing; and therefore in those cases in which the term whole is properly used, one complete thing is made from all the parts taken together, and the perfection of the whole belongs to none of the parts. A house and an animal are examples of this. Hence, “every animal” is not said of one animal but of many.
Therefore at the end of this part of his discussion he says that those wholes of which the term every is used, as is done of one thing when reference is made to a whole, can have the term all (in the plural) used of them, as is done of several things when reference is made to them as parts. For example, one says “all this number,” and “all these units,” and “all this water,” when the whole has been indicated, and “all these waters” when the parts have been indicated.
1109. It is not any quantity (522).
Here he clarifies the issue about the opposite of “whole,” which is mutilated, in place of which another translation reads “diminished (or reduced) by a member”; but this does not always fit. For the term mutilated is used only of animals, which alone have members. Now mutilated seems to mean “cut off,” and thus Boethius translated it “maimed,” i.e., “defective.” Hence the Philosopher’s aim here is to show what is required in order that a thing may be said to be mutilated: and first, what is required on the side of the whole; and second (1117), what is required on the side of the part which is missing (“Further, neither”).
1110. Now in order that a whole can be said to be mutilated, seven things are required.
First, the whole must be a quantified being having parts into which it may be divided quantitatively. For a universal whole cannot be said to be mutilated if one of its species is removed.
1111. Second, not every kind of quantified being can be said to be mutilated, but it must be one that is “ divisible into parts,” i.e., capable of being separated, and be “a whole,” i.e., something composed of different parts. Hence the ultimate parts into which any whole is divided, such as flesh and sinew, even though they have quantity, cannot be said to be mutilated.
1112. Third, (~) two things are not mutilated, i.e., anything having two parts, if one of them is taken away from the other. And this is true because a “mutilated part,” i.e., whatever is taken away from the mutilated thing, is never equal to the remainder, but the remainder must always be larger.
1113. Fourth, no (~) number can be mutilated no matter how many parts it may have, because the substance of the mutilated thing remains after the part is taken away. For example, when a goblet is mutilated it still remains a goblet; but a number does not remain the same no matter what part of it is taken away. For when a unit is added to or subtracted from a number, it changes the species of the number.
1114. Fifth, the thing mutilated must have unlike parts. For those things which have like parts cannot be said to be mutilated, because the nature of the whole remains verified in each part. Hence, if any of the parts are taken away, the others are not said to be mutilated. Not all things having unlike parts, however, can be said to be mutilated; for a number cannot, as has been stated, even though in a sense it has unlike parts; for example, the number twelve has the number two and the number three as parts of it. Yet in a sense every number has like parts because every number is constituted of units.
1115. Sixth, none of those things (~) in which the position of the parts makes no difference can be said to be mutilated, for example, water or fire. For mutilated things must be such that the intelligible structure of their substance contains the notion of a determinate arrangement of parts, as in the case of a man or of a house.
1116. Seventh, mutilated things must be continuous. For a musical harmony cannot be said to be mutilated when a note or a chord is taken away, even though it is made up of low and high pitched sounds, and even though its parts have a determinate position, it is not any low and high pitched sounds arranged in any way at all that constitute such a harmony.
1117. Further, neither is (523).
Then he indicates the conditions which must prevail with regard to the part cut off in order that a thing may be mutilated; and there are three of these. He says that, just as not every kind of whole can be said to be mutilated, so neither can there be mutilation by the removal of every part. For, first, the part which is removed must not be a (~) principal part of the substance, that is, one which constitutes the substance of the thing and without which the substance cannot be, because the thing that is mutilated must remain when a part is removed, as has been stated above (1113). Hence a man cannot be said to be mutilated when his head has been cut off.
1118. Second, the part removed should not be everywhere, but in some extremity. Thus, if a goblet is perforated about the middle by removing some part of it, it cannot be said to be mutilated; but this is said if someone removes “the ear of a goblet,” i.e., a part which is similar to an ear, or any other extremity. Similarly a man is not said to be mutilated if he loses some of his flesh from his leg or from his arm or from his waist, or if he loses his spleen or some part of it, but if he loses one of his extremities, such as a hand or a foot.
1118a. Third, a thing is not said to be mutilated if just any part that is an extremity is removed, but if it is such a part which does not regenerate if the whole of it is removed, as a hand or a foot. But if a whole head of hair is cut off, it grows again. So if such parts are removed, the man is not said to be mutilated, even though they are extremities. And for this reason people with shaven heads are not said to be mutilated.

LESSON 22
The Meanings of Genus, of Falsity, and of Accident
ARISTOTLE'S TEXT Chapters 28-30: 10-24a 29-1025a 34
524. The term genus (or race) is used if there is a continuous generation of things having the same species; for example, "as long as the genus of man lasts" means "while there is continuous generation of men." And the term also designates that from which things are first brought into being. For it is in this way that some men are called Hellenes by race and others Ionians, because the former come from Hellen and the latter from Ion as the ones who begot them. Again the term is applied to the members of the genus more from the begetter than from the material principle. For some people are also said to derive their race from the female, as those who come from Pleia. Further, the term is used in the sense that the plane is called the genus of plane figures, and the solid the genus of solid figures. For each of the figures is either a plane of such and such a kind or a solid of such and such a kind; and this is the subject underlying the differences. Again, genus means the primary element present in definitions, which is predicated quidditatively of the thing whose differences are called qualities. The term genus, then, is used in all these senses: in one as the continuous generation of a species; in another as the primary mover of the same species; and in another as matter. For that to which the difference or quality belongs is the subject which we call matter.
525. Things are said to be diverse (or other) in species whose first subject is diverse and cannot be resolved one into the other or both into the same thing. For example, form and matter are diverse in genus. And all things which are predicated according to a different categorical figure of being are diverse in genus. For some signify the quiddity of beings, others quality, and others something else, in the sense of our previous distinctions. For they are not analyzed into each other or into some one thing.
Chapter 29
526. False means in one sense what is false as a thing, and that either because it is not combined or is incapable of being combined. For example, the statement that the diagonal is commensurable or that you are sitting belong to this class; for the former is always false and the latter is sometimes so; for it is in these senses that these things are non-beings. But there are things which exist and are fitted by nature to appear either other than they are or as things that do not exist, as a shadowgraph and dreams. For these in fact are something, but not that of which they cause an image in us. Therefore things are said to be false either because they do not exist or because the image derived from them is not of something real.
527. A false notion inasmuch as it is false is the notion of something non-existent. Hence every notion is false when applied to something other than that of which it is true; for example, the notion of a circle is false when applied to a triangle. Now of each thing there is in a sense one notion, which is its essence; but there are also in a sense many, since the thing itself and the thing with a modification are in a sense the same, as Socrates and musical Socrates. But a false notion is absolutely speaking not the notion of anything. And it is for this reason that Antisthenes entertained a silly opinion when he thought that nothing could be expressed except by its proper notion—one term always for one thing. From this it would follow that there can be no contradiction and almost no error. It is possible, however, to express each thing not only by its own notion but also by that which belongs to something else not only falsely but also truly, as eight may be said to be double through the notion of two. These are the ways, then, in which things are said to be false.
528. A false man is one who chooses such thoughts not for any other reason but for themselves; and one who is the cause of such thoughts in others; just as we say that those things are false which produce a false image or impression.
529. Hence, the speech in the Hippias, which says that the same man is true and false, is refuted; for it assumes that that man is false who is able to deceive, even though he is knowing and prudent.
530. And further it assumes that one who is capable of willing evil things is better. And this false opinion is arrived at by way of induction. For one who limps voluntarily is better than one who does so involuntarily; and by limping we mean imitating a limp. For if a man were to limp voluntarily, he would be worse in this way, just as he would be in the case of moral character.
Chapter 30
531. An accident is what attaches to anything and which it is true to affirm is so, although not necessarily or for the most part; for example, if someone discovers a treasure while digging a hole for a plant, the discovery of the treasure is an accident to the digger. For the one does not necessarily come from the other or come after it, nor does it happen for the most part that someone will find a treasure when he digs a hole to set out a plant. And a musician may be white; but since this does not happen necessarily or for the most part, we say that it is accidental. But since something belongs to something, and some belong somewhere and at some time, then whatever attaches to a subject, but not because it is now or here,' will be an accident. Nor does an accident have any determinate cause, but only a contingent or chance cause, i.e., an indeterminate one. For it was by accident that someone came to Aegina; and if he did not come there in order to get there, but because he was driven there by a storm or was captured by pirates, the event has occurred and is an accident; yet not of itself but by reason of something else. For the storm is the cause of his coming to the place to which he was not sailing, and this was Aegina. And in another sense accident means whatever belongs to each thing of itself but not in its substance; for example, it is an accident of a triangle to have its angles equal to two right angles. And these same accidents may be eternal, but none of the others can be. But an account of this has been given elsewhere.
COMMENTARY
Genus
1119. Here he gives his views about a particular kind of whole, namely, a genus. First, he gives the different senses in which the term genus is used; and second (1124), he treats the different senses in which things are said to be diverse (or other) in genus (“Things are said”). He accordingly says, first, that the term genus is used in four senses:
First, it means the continuous generation of things that have the same species; for example, it is said, “as long as ‘the genus of man’ will exist,” i.e., “while the continuous generation of men will last.” This is the first sense of genus given in Porphyry, i.e., a multitude of things having a relation to each other and to one principle.
1120. In a second sense genus (race) means that from which “things are first brought into being,” i.e., some things proceed from a begetter. For example, some men are called Hellenes by race because they are descendants of a man called Hellen; and some are called Ionians by race because they are descendants of a certain Ion as their first begetter. Now people are more commonly named from their father, who is their begetter, than from their mother, who produces the matter of generation, although some derive the name of their race from the mother; for example, some are named from a certain woman called Pleia. This is the second sense of genus given in Porphyry.
1121. The term genus is used in a third sense when the surface or the plane is called the genus of plane figures, “and the solid,” or body, is called the genus of solid figures, or bodies. This sense of genus is not the one that signifies the essence of a species, as animal is the genus of man, but the one that is the proper subject in the species of different accidents. For surface is the subject of all plane figures. And it bears some likeness to a genus, because the proper subject is given in the definition of an accident just as a genus is given in the definition of a species. Hence the proper subject of an accident is predicated like a genus. “For each of the figures,” i.e., plane figures, is such and such a surface. “And this,” i.e., a solid figure, is such and such a solid, as though the figure were a difference qualifying surface or solid. For surface is related to plane (surface) figures, and solid to solid figures, as a genus, which is the subject of contraries; and difference is predicated in the sense of quality. And for this reason, just as when we say rational animal, such and such an animal is signified, so too when we say square surface, such and such a surface is signified.
1122. In a fourth sense genus means the primary element given in a definition, which is predicated quidditatively, and differences are its qualities. For example, in the definition of man, animal is given first and then two-footed or rational, which is a certain substantial quality of man.
1123. It is evident, then, that the term genus is used in so many different senses: (1) in one sense as the continuous generation of the same species, and this pertains to the first sense; (2) in another as the first moving principle, and this pertains to the second sense; (3&4) and in another as matter, and this pertains to the third and fourth senses. For a genus is related to a difference in the same way as a subject is to a quality. Hence it is evident that genus as a predicable and genus as a subject are included in a way under one meaning, and that each has the character of matter. For even though genus as a predicable is not matter, still it is taken from matter as difference is taken from form. For a thing is called an animal because it has a sentient nature; and it is called rational because it has a rational nature, which is related to sentient nature as form is to matter.
1124. Things are said (525).
Here he explains the different senses in which things are said to be diverse (or other) in genus; and he gives two senses of this corresponding to the last two senses of genus. For the first two senses are of little importance for the study of philosophy.
In the first sense, then, some things are said to be diverse in genus because their first subject is diverse; for example, the first subject of color is surface, and the first subject of flavors is something moist. Hence, with regard to their subject-genus, flavor and color are diverse in genus.
1125. Further, the two different subjects must be such that one of them is not reducible to the other. Now a solid is in a sense reducible to surfaces, and therefore solid figures and plane figures do not belong to diverse genera. Again, they must not be reducible to the same thing. For example, form and matter are diverse in genus if they are considered according to their own essence, because there is nothing common to both. And in a similar way the celestial bodies and lower bodies are diverse in genus inasmuch as they do not have a common matter.
1126. In another sense those things are said to be diverse in genus which are predicated “according to a different figure of the category of being,” i.e., of the predication of being. For some things signify quiddity, some quality, and some signify in other ways, which are given in the division made above where he dealt with being (889-94). For these categories are not reducible one to the other, because one is not included under the other. Nor are they reducible to some one thing, because there is not some one common genus for all the categories.
1127. Now it is clear, from what has been said, that some things are contained under one category and are in one genus in this second sense, although they are diverse in genus in the first sense. Examples of this are the celestial bodies and elemental bodies, and colors and flavors. The first way in which things are diverse in genus is considered rather by the natural scientist and also by the philosopher, because it is more real. But the second way in which things are diverse in genus is considered by the logician, because it is conceptual.
False
1128. “False” means (526).
Here he gives the various senses of the terms which signify a lack of being or incomplete being. First, he gives the senses in which the term false is used. Second (1139), he deals with the various senses of accident.
In regard to the first he does three things. First, he shows how the term false is used of real things; and second (1130), how it is used of definitions (“A false notion”); and third (1135), how men are said to be false (“A false man”).
He accordingly says, first, that the term false is applied in one sense to real things inasmuch as a statement signifying a reality is not properly composed. And there are two ways in which this can come about:
In one way by forming a proposition which should not be formed; and this is what happens, for instance, in the case of false contingent propositions. In another way by forming a proposition about something impossible; and this is what happens in the case of false impossible propositions. For if we say that the diagonal of a square is commensurable with one of its sides, it is a false impossible proposition; for it is impossible to combine “commensurable” and “diagonal.” And if someone says that you are sitting while you are standing, it is a false contingent proposition; for the predicate does not attach to the subject, although it is not impossible for it to do so. Hence one of these—the impossible—is always false; but the other—the contingent is not always so. Therefore those things are said to be false which are non-beings in their entirety; for a statement is said to be false when what is signified by the statement is nonexistent.
1129. The term false is applied to real things in a second way inasmuch as some things, though beings in themselves, are fitted by nature to appear either to, be other than they are or as things that do not exist, as “a shadowgraph,” i.e., a delineation in shadow. For sometimes shadows appear to be the things of which they are the shadows, as the shadow of a man appears to be a man. The same applies to dreams, which seem to be real things yet are only the likenesses of things. And one speaks in the same way of false gold, because it bears a resemblance to real gold. Now this sense differs from the first, because in the first sense things were said to be false because they did not exist, but here things are said to be false because, while being something in themselves, they are not the things “of which they cause an image,” i.e., which they resemble.
It is clear, then, that things are said to be false (1) either because they do not exist or (2) because there arises from them the appearance of what does not exist.
1130. A “false” notion (527).
He indicates how the term false applies to definitions. He says that “a notion,” i.e., a definition, inasmuch as it is false, is the notion of something non-existent. Now he says “inasmuch as it is false” because a definition is said to be false in two ways:
It is either a false definition in itself, and then it is not the definition of anything but has to do entirely with the nonexistent; or it is a true definition in itself but false inasmuch as it is attributed to something other than the one properly defined; and then it is said to be false inasmuch as it does not apply to the thing defined.
1131. It is clear, then, that every definition which is a true definition of one thing is a false definition of something else; for example, the definition which is true of a circle is false when applied to a triangle. Now for one thing there is, in one sense, only one definition signifying its quiddity; and in another sense there are many definitions for one thing. For in one sense the subject taken in itself and “the thing with a modification,” i.e., taken in conjunction with a modification, are the same, as Socrates and musical Socrates. But in another sense they are not, for it is the same thing accidentally but not in itself. And it is clear that they have different definitions. For the definition of Socrates and that of musical Socrates are different, although in a sense both are definitions of the same thing.
1132. But a definition which is false in itself cannot be a definition of anything. And a definition is said to be false in itself, or unqualifiedly false, by reason of the fact that one part of it cannot stand with the other; and such a definition would be had, for example, if one were to say “inanimate living thing.”
1133. Again, it is clear from this that Antisthenes’ opinion was foolish. For, since words are the signs of things, he maintained that, just as a thing does not have any essence other than its own, so too in a proposition nothing can be predicated of a subject but its own definition, so that only one predicate absolutely or always may be used of one subject. And from this position it follows that there is no such thing as a contradiction; because if animal, which is included in his notion, is predicated of man, non-animal can not be predicated of him, and thus a negative proposition cannot be formed. And from this position it also follows that one cannot speak falsely, because the proper definition of a thing is truly predicated of it. Hence, if only a thing’s own definition can be predicated of it, no proposition can be false.
1134. But his opinion is false, because of each thing we can predicate not only its own definition but also the definition of something else. And when this occurs in a universal or general way, the predication is false. Yet in a way there can be a true predication; for example, eight is said to be double inasmuch as it has the character of duality, because the character of duality is to be related as two is to one. But inasmuch as it is double, eight is in a sense two, because it is divided into two equal quantities. These things, then, are said to be false in the foregoing way.
1135. Then he shows how the term false may be predicated of a man; and in regard to this he does two things. First, he gives two ways in which a man is said to be false. (1) In one way a man is said to be false if he is ready to think, or takes pleasure in thinking, thoughts of this kind, i.e., false ones, and chooses such thoughts not for any other reason but for themselves. For anyone who has a habit finds the operation relating to that habit to be pleasurable and readily performed; and thus one who has a habit acts in accordance with that habit and not for the sake of anything extrinsic. For example, a debauched person commits fornication because of the pleasure resulting from coition; but if he commits fornication for some other end, for instance, that he may steal, he is more of a thief than a lecher. And similarly one who chooses to speak falsely for the sake of money is more avaricious than false.
1136. (2) In a second way a man is said to be false if he causes false notions in others, in much the same way as we said above that things are false which cause a false image or impression. For it is clear from what has been said that the false has to do with the non-existent. Hence a man is said to be false inasmuch as he makes false statements, and a notion is said to be false inasmuch as it is about something nonexistent.
1137. Hence, the speech (529).
Second, he excludes two false opinions from what has been laid down above. He draws the first of these from the points made above. He says that, since a false man is one who chooses and creates false opinions, one may logically refute or reject a statement made in the Hippias, i.e., one of Plato’s works, which said that the same notion is both true and false. For this opinion considered that man to be false who is able to deceive, so that, being able both to deceive and to speak the truth, the same man is both true and false. And similarly the same statement will be both true and false, because the same statement is able to be both true and false; for example, the statement “Socrates sits” is true when he is seated, but is false when he is not seated. Now it is evident that this is taken unwarrantedly, because even a man who is prudent and knowing is able to deceive; yet he is not false, because he does not cause or choose false notions or opinions, and this is the reason why a man is said to be false, as has been stated (1135).
1138. And further (530).
Then he rejects the second false opinion. This opinion maintained that a man who does base things and wills evil is better than one who does not But this is false. For anyone is defined as being evil on the grounds that he is ready to do or to choose evil things. Yet this opinion wishes to accept this sense of false on the basis of a sort of induction from a similar case. For one who voluntarily limps is better and nobler than one who limps involuntarily: Hence he says that to do evil is like limping inasmuch as the same notion applies to both. And in a sense this is true; for one who limps voluntarily is worse as regards his moral character, although he is more perfect as regards his power of walking. And similarly one who voluntarily does evil is worse as regards his moral character, although perhaps he is not worse as regards some other power. For example, even though that man is more evil, morally speaking, who voluntarily says what is false, still he is more intelligent than one who believes that he speaks the truth when he in fact speaks falsely, though not wilfully.
Accident
1139. An “accident” (531).
Here, finally, he gives the different senses in which the term accident is used; and there are two of these:
(1) First, an accident means anything that attaches to a thing and is truly affirmed of it, although not necessarily or “for the most part,” i.e., in the majority of cases, but in a minority; for example, if one were to find a treasure while digging a hole to set out a plant. Hence, finding a treasure while (digging a hole is an accident. For the one is not necessarily the cause of the other so that the one necessarily comes from the other. Neither do they necessarily accompany each other so that the latter comes after the former as day follows night, even though the one is not the cause of the other. Neither does it happen for the most part, or in the majority of cases, that this should occur, i.e., that one who sets out a plant finds a treasure. And similarly a musician is said to be white, although this is not necessarily so nor does it happen for the most part. Hence our statement is accidental. But this example differs from the first; for in the first example the term accident is taken in reference to becoming, and in the second example it is taken in reference to being.
1140. Now just as something belongs to some definite subject, so too it is considered “to belong somewhere,” i.e., in some definite place, “and at some time,” i.e., at some definite time. And therefore it happens to belong to all of these accidentally if it does not belong to them by reason of their own nature; for example, when white is predicated of a musician, this is accidental, because white does not belong to a musician as such. And similarly if there is an abundance of rain in summer, this is accidental, because it does not happen in summer inasmuch as it is summer. And again if what is heavy is high up, this is accidental, for it is not in such a place inasmuch as the place is such, but because of some external cause.
1141. And it should be borne in mind that there is no determinate cause of the kind of accident here mentioned, “but only a contingent cause,” i.e., whatever one there happens to be, or “a chance cause,” i.e., a fortuitous one, which is an indeterminate cause. For example, it was an accident that someone “came to Aegina,” i.e., to that city, if he did not come there “in order to get there,” i.e., if he began to head for that city not in order that he might reach it but because he was forced there by some external cause; for example, because he was driven there by the winter wind which caused a tempest at sea, or even because he was captured by pirates and was brought there against his will. It is clear, then, that this is accidental, and that it can be brought about by different causes. Yet the fact that in sailing he reaches this place occurs “not of itself,” i.e., inasmuch as he was sailing (since he intended to sail to another place), but “by reason of something else,” i.e., another external cause. For a storm is the cause of his coming to the place “to which he was not sailing,” i.e., Aegina; or pirates; or something else of this kind.
1142. (2) [ property ] In a second sense accident means whatever belongs to each thing of itself but is not in its substance. This is the second mode of essential predication, as was noted above (1055); for the first mode exists when something is predicated essentially of something which is given in its definition, as animal is predicated of man, which is not an accident in any way. Now it belongs essentially to a triangle to have two right angles, but this does not belong to its substance. Hence it is an accident.
1143. This sense of accident differs from the first, because accidents in this second sense can be eternal. For a triangle always has three angles equal to two right angles. But none of those things which are accidents in the first sense can be eternal, because they are always such as occur in the minority of cases. The discussion of this kind of accident is undertaken in another place, for example in Book VI of this work (1172), and in Book II of the Physics. Accident in the first sense, then, is opposed to what exists in itself; but accident in the second sense is opposed to what is substantial. This completes Book V.

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LESSON 1:	Five Senses of the Term "Principle." The Common Definition of Principle
LESSON 2	The Four Classes of Causes. Several Causes of the Same Effect. Causes May Be Causes of Each Other. Contraries Have the Same Cause
LESSON 3	All Causes Reduced to Four Classes
LESSON 4	The Proper Meaning of Element; Elements in Words, Natural Bodies, and Demonstrations. Transferred Usages of "Element" and Their Common Basis
LESSON 5	Five Senses of the Term Nature
LESSON 6	Four Senses of the Term Necessary. Its First and Proper Sense. Immobile Things, though Necessary, Are Exempted from Force
LESSON 7	The Kinds of Accidental Unity and of Essential Unity
LESSON 8	The Primary Sense of One. One in the Sense of Complete. One as the Principle of Number. The Ways in Which Things Are One. The Ways in Which Things Are Many
LESSON 9	Division of Being into Accidental and Essential. The Types of Accidental and of Essential Being
LESSON 10	Meanings of Substance
LESSON 11	The Ways in Which Things Are the Same Essentially and Accidentally
LESSON 12	Various Senses of Diverse, Different, Like, Contrary, and Diverse in Species
LESSON 13	The Ways in Which Things Are Prior and Subsequent
LESSON 14	Various Senses of the Terms Potency, Capable, Incapable, Possible and Impossible
LESSON 15	The Meaning of Quantity. Its Kinds. The Essentially and Accidentally Quantitative
LESSON 16	The Senses of Quality
LESSON 17	The Senses of Relative
LESSON 18	The Senses of Perfect
LESSON 19	The Senses of Limit, of "According to Which," of "In Itself," and of Disposition
LESSON 20	The Meanings of Disposition, of Having, of Affection, of Privation, and of "To Have"
LESSON 21	The Meanings of "To Come from Something," Part, Whole, and Mutilated
LESSON 22	The Meanings of Genus, of Falsity, and of Accident

METAPHYSICS BOOK V

DEFINITIONS

METAPHYSICS
BOOK V